You Get What You Give: Theory and Evidence of
Reciprocity in the Sharing Economy
Davide Proserpio
Marshall School of Business
University of Southern California
Wendy Xu
Department of Economics
Boston University
Georgios Zervas
Questrom School of Business
Boston University∗
November 15, 2016
Abstract
This paper provides evidence on the importance of user interaction in the sharing
economy. We develop an analytical framework incorporating reciprocity, the tendency
to increase effort in response to others’ increased efforts. In our model, buyers (sellers) can induce sellers (buyers) to exert more effort by behaving well themselves. We
demonstrate that this joint increased effort improves the utility of both parties and
influences the market equilibrium. Moreover, we show that reciprocity becomes more
salient in the sharing economy compared to traditional marketplaces for similar services,
generating trust among strangers and informally regulating their behavior. Finally, we
test the predictions of our model using data from Airbnb, a popular peer-to-peer rental
accommodation platform.
∗
Authors contributed equally to the paper, and are listed in alphabetical order.
1
1
Introduction
Over the past few years, we have witnessed the rapid growth of peer-to-peer marketplaces
like Airbnb (accommodation), Uber (transportation), and TaskRabbit (chores and errands).
Compared to traditional marketplaces for similar services, peer-to-peer markets have two
distinguishing features. First, service quality is heterogeneous and can vary significantly
both between suppliers and from one occasion to the next. Second, transactions in peerto-peer markets entail the close interaction of buyers and sellers. In this paper, we study
these user interaction patterns, focusing in particular on reciprocity: the ability of market
participants to reward good behavior and punish bad behavior. We provide theoretical and
empirical evidence that reciprocity regulates the behavior of peer-to-peer market participants
and facilitates successful market outcomes in a setting where quality is uncertain.
The sharing economy is a natural setting for reciprocity to arise. Take for instance
Airbnb, an online marketplace for short-term accommodation rentals that has emerged as
an alternative to hotels (Zervas et al., 2015b). According to Airbnb, most hosts rent the place
they live in, and are likely to closely interact with their guests.1 Some Airbnb hosts provide
home cooked meals, take their guests on neighborhood tours, or pick their guests up from
the airport. Airbnb guests can reward exceptional hospitality by keeping the place clean,
being respectful of neighbors, or leaving small gifts for their hosts. Airbnb user testimonials
suggest that this type of behavior is both common and greatly valued by guests and hosts
alike.2 In this paper, we develop an analytical model of reciprocity in peer-to-peer markets,
and use data from Airbnb to both motivate and test our theory.
To motivate the need for incorporating reciprocity in models of peer-to-peer market
user behavior, consider the following two empirical observations. First, it has been shown
that ratings – the primary signal of quality – are informative in the sense that they can
reliably predict certain measures of customer satisfaction, such as the probability of placing
a customer service call (Fradkin et al., 2015; Horton and Golden, 2015). Further, in this
paper, we provide new evidence that ratings are informative by showing that Airbnb ratings
directly affect prices. Second, we report a new and intriguing finding: Airbnb hosts with
more frequent market participation have lower ratings than more casual hosts. Moreover,
this relationship is independent of the degree of social interaction between guests and hosts,
and thus unlikely to be attributable to social bias arising from the face-to-face interaction
between hosts and guest (Fradkin et al., 2015). Taken together these two observations would
suggest that casual hosts offer higher levels of quality than professional hosts.
1
2
See http://blog.airbnb.com/economic-impact-airbnb/.
See, for instance, https://www.airbnb.com/info/why_host.
2
At first, this finding may seem surprising: hosts who regularly make their properties
available for rent are more reliant on Airbnb income and should, therefore, strive to earn
higher ratings than casual hosts. However, we claim that this seemingly unintuitive fact is
the result of reciprocity, a feature of market participants’ preferences which Sobel (2005)
defines as the “tendency to respond to good conduct with good conduct and meanness with
meanness”. We argue that on Airbnb, casual hosts are more sensitive to guest conduct, and
thus, are more likely to reciprocate good guest behavior, which results in casual hosts earning
higher ratings than more frequent market participants.
We formalize this intuition by developing an analytical framework of user interaction in
the sharing economy. Taking Airbnb as our use case, we model the quality of each Airbnb
stay as a function of the joint effort of hosts and guests. In deciding how much effort to
exert during each stay, hosts and guests take into account each others’ reciprocal preferences.
These preferences can vary. For example, some hosts will respond to a small gift by taking
better care of their guests, while others won’t. Airbnb guests can induce reciprocal hosts
to exert more effort by behaving better themselves. Reciprocal hosts respond to increased
guest effort by increasing their own effort levels and, as a result, earn higher ratings from
their guests. Therefore, in our model hosts who are more reciprocal have higher ratings.
In turn, higher ratings in our model lead to increases in demand and, consequently, more
reciprocal hosts can charge higher prices. Consequently, our model predicts that reciprocity
influences market prices through its effect on ratings.
Besides its impact on market equilibrium and prices, reciprocity in the sharing economy
can act as a social norm, generating trust between market participants (Malmendier et al.,
2014). When two agents trade, one agent’s poor conduct can trigger negative reciprocity and
the agent is punished by the other party. Similarly, an agent’s good conduct triggers positive
reciprocity and the agent is rewarded by other party. Thus, agents may choose to behave
well both to motivate good conduct back and to avoid the threat of negative reciprocity.
Through this mechanism, reciprocity can regulate behavior and generate trust among users.
In this sense, our work contributes to a more comprehensive understanding on how trust is
generated in peer-to-peer markets (Tadelis, 2016).
We use data from Airbnb to test the predictions of our model in the field. To show that
reciprocity affects ratings, we begin by identifying subsets of Airbnb hosts who are likely
to be reciprocal, i.e., hosts who value their guests’ behavior. Because we cannot directly
measure reciprocity, we rely on proxies. Our preferred proxy is the length of the reviews hosts
leave for their guests. Unlike listing reviews, which usually describe both the host and her
property, guest reviews describe the person being accommodated. Therefore, we hypothesize
that hosts who take the time to write detailed reviews about their guests, are more likely to
3
care about their guests’ conduct, i.e., to value reciprocity more. As hypothesized, we find
that hosts who write longer guest reviews have higher ratings. We show that this result is
robust to alternative proxies for reciprocity.
Next, we use this result to support our motivating hypothesis that casual Airbnb hosts are
likely to have higher ratings because they are more reciprocal than professional hosts. To do
so, we show that our proxies for reciprocity are negatively correlated with listing availability.
Thus, the better ratings of casual hosts can be in part explained by their increased preference
for reciprocity.
Finally, we test our model’s prediction that prices should respond positively to ratings,
thus affecting market equilibrium. To do so, we exploit a unique feature of the Airbnb
reputation system: Airbnb discloses a host’s rating only after the host collects three reviews.
We treat these rating disclosures as natural experiments, and show that listing prices respond
positively to the disclosure of high ratings, even after controlling for changes in listing quality.
Our model of reciprocity can also be applied to settings beyond sharing economy. A
number of papers have studied the effect of reciprocity in the labor market (Irlenbusch and
Ruchala, 2008; Kirchler et al., 1996), organizational economics (Ellingsen and Johannesson,
2006)) and economics of education (Almlund et al., 2011). These models differ from our
framework in that they typically study settings where only agents have superior private
information and thus they are endowed with reciprocity, while the principals are still assumed
to be caring about their profit. However, when the information asymmetry problem is
bilateral, i.e., both sides have private information (such as in sharing economy platforms)
it is natural to hypothesize that the agent’s rationale to be reciprocal can also motivate
the principal to be reciprocal. Therefore, our model of reciprocity can be applied in these
principal-agent settings to model cooperation and mutual trust between principal and agents.
Our work also contributes to the existing research on reciprocity by not invoking signaling, belief manipulation, or imperfect recall, such as models built upon psychological game
theory (Charness and Dufwenberg, 2008). By comparison, our model is context-independent
and free from signaling. Further, our model is also the first, to the best of our knowledge,
to apply interdependent preference to study the sharing economy, and to show that this
interdependence is more salient in these new marketplaces.
4
2
Airbnb and data
2.1
Airbnb
We use data from Airbnb to motivate our model and test its predictions. Airbnb, which
launched in 2008, is a peer-to-peer marketplace for short term accommodation rentals.
Airbnb hosts offer private or shared accommodation for rent to prospective guests. The
Airbnb marketplace has seen a dramatic growth over the last few years. At the beginning
of 2016 the platform listed approximately 2 million properties from 640,000 hosts in over
150,000 cities and 52 countries.3 Over 60 million guests has used Airbnb, and with a market
valuation of $25B, Airbnb is one of the world’s largest accommodation brands.4
To build trust among users, Airbnb uses a bilateral rating system. Hosts and guests
can optionally review each other, and these reviews are publicly disclosed. Prior to July
2014, Airbnb users had the option of reviewing each other within a 30-day window following
the conclusion of each stay. During this 30-day window, reviews were revealed as they
were submitted. This sequential revelation mechanism allowed for retaliatory reviewing: the
second reviewer could punish the first reviewer by submitting a negative review in exchange
for receiving a negative review. (Fradkin et al., 2015). In July 2014 Airbnb made a major
change to its reputation system: Airbnb shortened the review window to 14 days, and started
revealing reviews only after the review submission window expired. In doing so, Airbnb
lessened the possibility of retaliatory reviewing.5 To reduce the possibility of analyzing
ratings that biased by strategic reviewing, we limit our dataset to hosts that entered the
Airbnb marketplace from July 2014 onwards.
2.2
Data
Our dataset is a weekly panel of US Airbnb listings spanning a 17-month period from the
beginning of July 2014 to the end of November 2015. During this timeframe, we collected
information on all US listings and their hosts from the Airbnb website with weekly frequency.
The final panel contains 3, 295, 188 listing-week observations for 198, 743 distinct listings
and 137, 687 distinct hosts, whose accounts were created on or after July 1, 2014. For each
listing, we observe various characteristics including location, listing type (e.g., apartment,
igloo, etc.), bed type, number of listing photos, price, star-rating, and number of reviews.
Additionally, for each host, we observe reviews left and received, and the number of properties
3
See: http://expandedramblings.com/index.php/airbnb-statistics/
See
http://qz.com/329735/airbnb-will-soon-be-booking-more-rooms-than-the-worldslargest-hotel-chains/
5
See: http://blog.airbnb.com/building-trust-new-review-system/
4
5
listed by the host on Airbnb.
Airbnb allows hosts to select which days of the year their listing are available for rent
without the need to add or remove the listing from the platform. To do so, hosts use a
calendar, on which they mark available days and set prices. In addition, Airbnb hosts can
make their listings instantly bookable, forgoing the opportunity to reject guests. We collected
calendar information (whether a listing was available for booking, booked, or busy) between
from September 2014 to September 2015. Given this data, we define listing availability as
the fraction of days the property was listed for rent or was rented, over the total number of
days the listing was available for rent. The final dataset contains availability information for
101, 596 listings and 74, 909 hosts. Out of these listings, 51, 697 have a star-rating (Airbnb
only assigns star-rating to listings with at least three reviews.) In Figure 1 we plot the
rating distribution for the subset of listings for which we know both their availability and
star-rating. As in previous work (Fradkin et al., 2015; Zervas et al., 2015a), we find that
most of the listings (91.7%) have a star-rating greater or equal than 4.5-stars. In Figure 2 we
plot the probability density function of the listing availability for the same subset of listings,
and find that, on average, a listing is available on the platform 85% of the time.
For every listing in our panel data we have on average 16 weekly observations. During
the period covered by our panel data, 107, 961 listings (and 83, 091 hosts) received at least
a review from a guest, while 67, 634 listings have a visible star-rating (which implies at least
3 reviews.) The average listing price observed in our data is $229, the average number of
reviews hosts received from guests is 4.53, and the average star-rating is 4.73. On average,
hosts write reviews that are shorter than the reviews they receive. On average, hosts in our
data received reviews with an average length of 351 characters, but left reviews only 151
characters long. Finally, by November 2015, the Instant Book feature is active for 30, 767
listings.
3
Motivating facts
In this section we motivate our analytical model by analyzing Airbnb ratings, and discuss
two empirical facts that cannot be easily explained under models that do not consider users’
reciprocal behavior.
3.1
Professional hosts have lower ratings than hosts
In this paper, we characterize the hosts by how often they participate in the market – the
fraction of days over the entire year they list their property for rent on the market. We refer
6
to hosts with high market participation as professional hosts and those with low market
participation as casual hosts. In Figure 3 we show that casual hosts have higher ratings than
professional hosts. In standard models, sellers are profit maximizers and therefore higher
participation in the market is generally associated with higher incentives to maintain high
ratings, contrasting the trend observed in our data.
How can we explain the negative relationship between market participation and rating?
One possibility may be socially induced bias: the tendency of Airbnb stays that involve more
face-to-face interaction to result in higher ratings (Fradkin et al., 2015). If professional hosts
are less likely to socially interact with their guests than a causal hosts, then socially induced
bias can explain the pattern observed we observe Figure 3. We test the social bias hypothesis
using the same proxy for face-to-face interaction as Fradkin et al. (2015). Specifically, we
divide hosts by the number listings they own, expecting more social interaction for singlelisting hosts than multi-listing hosts. However, as see in Figures 4 and 5) the relationship
between availability and rating remains for both types of hosts. Thus, socially-induced bias
is unlikely to fully explain the rating patterns we observe.
3.2
Rating are informative
The second fact motivating our work is the informativeness of Airbnb ratings. Fradkin et al.
(2015) show that Airbnb ratings are informative about listing quality because they predict
customer service calls during a transaction and guest rebooking rates of guests. If ratings
are a signal for quality, and because professional hosts have lower ratings than casual hosts,
we can deduce that, on average, professional hosts provide lower quality than casual hosts.
However, this is not what one would expect to observe: because professional hosts heavily
depend on Airbnb profits, they should strive to maintain high quality and therefore ratings,
which in turn translate to high demand and revenue.
3.3
Reconciling empirical facts
In this paper, we propose a novel analytical framework that introduces reciprocity to model
the social interaction between buyers and sellers on Airbnb. Our model can explain the rating
patterns observed in the field. Before presenting our model of reciprocity, we first consider
alternative models to explain the empirical facts observed on Airbnb, and informally show
that none of them can easily reconcile the rating patterns we observe. Then, we provide some
insights on why introducing reciprocity is an intuitive choice for modeling the user interaction
on Airbnb. For a formal analysis including proofs, we refer the reader to Appendix A.
7
3.3.1
Simple model
We start with a simple model where service quality is private information of the host, and
guests infer this hidden information from publicly available ratings. Service quality is exogenously given and fixed across transactions. We also assume a monopoly host who maximizes
expected profits by choosing prices. All players report their utility in their ratings.
In this model, in order to explain the fact that casual hosts have higher ratings than professional hosts, we need to assume that casual hosts provide higher service quality. However,
since the main difference between professional and casual hosts is their market participation,
we expect these two host types to differ mainly in how much they care about profits, instead
of the exogenously given service quality.6 In other words, this model does not provide a
direct connection between the service quality provided and the host’s weight on reputation.
Thus, it cannot justify why casual hosts, who generally have lower weight on reputation than
professional hosts, have higher ratings.7
Next, we extend the simple model by introducing selection bias in the ratings, and show
that it does not help to explain the pattern observed. Selection bias can be introduced
by relaxing the assumption that guests report their utility in their ratings. Under this
assumption, guests incur a psychological cost associated with giving low ratings, and hence,
only high ratings are reported. In this variant of the benchmark model, to explain that casual
hosts have higher ratings than professional hosts, we need to assume that they are more likely
to interact with guests with higher psychological cost than professional hosts. Therefore, the
difference in ratings between the two host categories is the result solely of selection bias,
which drastically reduces the rating informativeness, contradicting the empirical facts.
3.3.2
Endogenizing the service quality
Next, we modify the simple model by relaxing the assumption that service quality is exogenously given and fixed across transactions. We assume that the service quality, modeled as
the effort exerted by the host in each transaction, is endogenously chosen, and can vary from
one transaction to the other. This is a natural choice in marketplaces like Airbnb, where
transactions are among peers, and service quality can vary substantially both between and
within suppliers.
In this model, guests report the host’s effort in their ratings. Therefore, since future
guests infer the host’s service quality from the ratings disclosed, higher ratings generate
higher expected demand. In this situation, ratings incentivize hosts to exert effort. Because
6
Simply stated, professional hosts who rely more on Airbnb revenue that casual hosts should strive to
maintain higher ratings, which translate to higher demand.
7
This rationale is robust to whether hosts are risk neutral or risk averse towards the guests’ behaviors.
8
professional hosts rely more heavily on Airbnb revenue than casual hosts, they have stronger
incentives to exert higher levels of effort, which translates to higher ratings and higher
demand, contradicting the empirical facts. Stated differently, a model where reputation is
the sole incentive of the effort exerted does not justify the higher ratings of casual hosts who
generally have fewer reputation concerns than professional hosts.
3.3.3
Introducing interdependent preference
In the preceding discussion, we have shown that endogenizing the service quality provides a
useful link between reputation concerns and the host’s effort. However, we have also shown
that this connection is not enough to reconcile the empirical facts. What we really need is
an incentive under which hosts who gain less from reputation, such as casual hosts, exert
more effort than hosts who gain more from reputation, such as professional hosts. Among
several possible incentives for the hosts to exert effort, one that fits well within the Airbnb
setting is the social preference. We model social preference by introducing interdependent
preference for the host. As a first attempt, we consider a model where the host internalizes
the guest’s utility in her own utility. By internalizing, we imply that guest utility enters
the host’s utility function, and different hosts place different weights on this term. Thus, in
this model, to show that casual hosts have higher ratings than professional hosts, we need
to assume that they have a higher weight on the guests’ welfare than professional hosts. In
other words, this is similar to saying that casual hosts are more altruistic. While this could
be true, we claim that altruistic behavior, where the host behaves better independently of
the guest’s behavior is not a rational behavior, and does not capture the user interaction on
Airbnb.
Thus, we propose a different interdependent model which incorporates reciprocity, and
argue that this model better captures the dynamics of the transactions on Airbnb, and more
in general of the sharing economy. Airbnb hosts generally rent the property they live in,8
and can provide different various courtesy services such as home cooked meals, neighborhood tours, and airport pick ups. Airbnb guests tend to respond to superior hospitality by
keeping the place clean, being respectful of the neighbors, or leaving small gifts for their
hosts.9 Moreover, Airbnb transactions occur between peers and hence, asymmetries between
buyers and sellers are much lower than in more traditional settings (such as hotels and their
customers.) This condition gives ample room for reciprocity to arise.10 Under the reciprocity
assumption, the conduct of a guest can affect the effort exerted by the host, i.e., good guest
8
See: http://blog.airbnb.com/economic-impact-airbnb/.
See: https://www.airbnb.com/info/why_host.
10
As discussed in Sobel (2005), one important reason for which reciprocity is difficult to observe in
traditional markets is because of “the asymmetries between buyers and sellers in the market”.
9
9
behavior will motivate a host to behave better and vice versa. We discuss this model in
detail next.
4
Theoretical framework
In this section we introduce our theoretical framework. Below, we describe the model in the
setting of Airbnb, but the model can be easily extended to other sharing economy platforms,
such as TaskRabbit or Upwork.
4.1
Setup
Since our goal is to describe the interaction between hosts and guests, in our analyses we
assume a monopolistic host, and a continuum of guests. Prices are posted by the host, which
matches the price-posting feature on Airbnb.
Our model has three periods:
1. In period 1, the host chooses price P1 for her listing, and every customer decides
whether to enter the market, i.e., pay the host to book the accommodation.
2. In period 2 (the accommodation period), the guest stays at host’s listing. Both the
host and the guest i determine the effort level to exert during the stay. Then, each
guest i who stays at the host’s property publishes a rating rh,i , and the host publishes
a rating ri for the guest i.
3. In period 3, another unit mass of guests enters the market. The host and period 3
guests observe the first period demand and the average rating disclosed in period 2.
The host chooses price P3 for her listing, and the customers decide whether to enter
the market according to the disclosed rating and the price observed.
Our analyses primarily focuses on period 2, and we solve the equilibrium by backward
induction from period 2 to period 1. Thus, in the following analyses, we introduce the setup
of period 2 first.
4.1.1
Period 2 (Accommodation)
In period 2, the guest and the host both choose their effort levels by maximizing their
respective ex-post utility:
Ui (ei |eh , ri ) = vh + αi u(ei , eh ) − Ci (ei ) + βi ri
10
(1)
Uh (eh |ei , rh,i ) = vi + αh u(ei , eh ) − Ch (eh ) + βh rh,i
(2)
Both utility functions are composed of three parts. The first part, vj + αj u(ei , eh ), is
the utility obtained from the accommodation stay; the second part, Cj (ej ), is the effort
cost; and the third part, rj , is the utility obtained from the ratings and reviews. While all
the alternative models considered in Section 3.3 have these three components, our model
innovates in the term αj u(ei , eh ). The term u(ei , eh ) represents the shared experience utility,
the parameter αj denotes the weight of the agent j puts on the shared experience and is also
called weight on reciprocity in later analysis. vj is the exogenous objective factor affecting
the accommodation, and also appears in the alternative models considered. For example, vh
can be the location of the listing property. Similarly, vi in equation 2 refers to some factors
of the guest i that affect the host’s utility and that are not endogenously determined by the
guest’ effort. An example of vi is whether the guest has a kid or a pet. Note that the terms
vh and vi are introduced to match a real scenario on Airbnb, but all of our analytical results
are robust to the presence of vi and vh .
The term βj denotes the weight of the reputation utility with respect to Uj , i.e., how
much agent j cares about the ratings and reviews she receives. The Equations 1 and 2 have
a reduced form of reputation concern, ri and rh,i , respectively. We introduce the reduced
form for tractability in showing that the different sensitivity of bilateral reputation system
on host’s two-dimension characteristics: reciprocity and reputation concerns. We discuss
this results in detail when we introduce Proposition 2 (Section 4.2). Also, we still follow
the standard rationale that the ratings determine future demand, and that this is why hosts
care about ratings.
The term u(ei , eh ) introduced above, the shared experience utility, represents the quality
of the stay which affects the welfare of both the host and the guest. It is determined by the
efforts of the host, denoted as eh , and the effort of the guest, denoted as ei . Examples of
eh on Airbnb include a smooth check-in/check-out, reserving a cab for the guest and tips
about restaurants in the neighborhood. Similarly, examples of ei include the guest effort to
be respectful and clean, or to follow the house rules.
We assume that both the host and guest efforts can improve the shared experience, i.e.:
∂u(ei , eh )
>0
∂ei
∂u(ei , eh )
> 0,
∂eh
(3)
(4)
which state that u(ei , eh ) increases with regard to ei and eh . Further, we model reciprocity
11
by assuming:
∂ 2 u(ei , eh )
> 0.
∂ei ∂eh
(5)
This condition states that a higher effort exerted by the host increases the marginal utility
of the well-behaved guest, i.e.,
0
if eh > eh , then
∂u(ei ,eh )
∂ei
0
>
∂u(ei ,eh )
,
∂ei
given the same level of ei .
Analogously, we also have a similar condition that higher efforts of the guests increases
the marginal utility of the host. This assumption is as with that of intrinsic reciprocity
models, such as the intention-based reciprocity (Rabin, 1993), and shows that an agent is
more willing to behave well to those agents that behave well to her.
Finally, we adopt the standard assumption that agents report their utility of the accommodation experience in the online ratings (to which we refer as the truth-telling assumption
in our analyses), i.e.,
ri = vi + αh u(ei , eh )
(6)
rh,i = vh + αi u(ei , eh ).
(7)
In Section 4.3, we show that our model is robust to the relaxation of such assumption.
In the analyses below, we adopt the widely-used quadratic functional form for the effort
c
cost function, i.e., Cj (ej ) = 2j e2j . Let Γj ≡ [αj , βj , cj , vj ], this vector is private information of
agent j, but its distribution is common knowledge. The joint cumulative distribution function
of Γh is denoted as F (Γh ). The parameter of guest i, Γi , follows F (Γg ), ∀i. Specifically, we
assume vh in Equation 1 and vi in Equation 2 to be private information of host and guest i,
fixed and exogenously given, and follow uniform distributions over [0, v¯h ] and over [0, v¯g ].
4.1.2
Period 1 (Pre-accommodation)
In period 1, the host posts the price P1 , and the guests decide whether to request accommodation. The transaction volume Q1 is determined at this stage. The utility of the host is
composed of two parts: the monetary revenue, P1 Q1 , and the expected utility in period 2.
The utility of the host in period 1 is given by:
ˆ
Vh (P1 ) = P1 Q1 +
Uh (e∗h , ei , vi , rh,i )dF (Γg ),
(8)
where Uh (e∗h , ei , vi , rh,i ) is the ex-post utility the host obtains during the period 2. e∗h is the
optimal effort the host exerts during the transaction with guest i; ei is the equilibrium effort
12
exerted by guest i, vi is the objective factor of guest i affecting the welfare of the host, and
rh,i is the rating the host gets from guest i.
In period 1, the early guests choose whether to make a booking request based on their
ex-ante utility. The ex-ante utility of guest i who chooses to enter the market is given by:
ˆ
Vi (P1 ) =
Ui (e∗i , eh , vh , ri )dF (Γh ) − P1 ,
(9)
where Ui (e∗i , eh , vh , ri ) is the ex-post utility of period 2. As before, the ex-post utility depends
on e∗i , the optimal effort exerted by guest i; eh , the equilibrium effort level exerted by the
host in the transaction with guest i, and ri , the rating guest i receives and vh .
4.2
Propositions
To simplify the mathematical proofs, in the following analyses we assume that the shared
experience utility takes the Cobb-Douglas functional form , i.e.,
u(ei , eh ) = eki e1−k
h , k ∈ (0, 1).
(10)
However, our model predictions suffice in any non-separable form of u(ei , eh ) satisfying the
following conditions:
∂u(ei , eh )
∂u(ei , eh )
∂ 2 u(ei , eh )
> 0,
> 0,
> 0.
∂ei ∂eh
∂ei
∂eh
(11)
We solve the equilibrium by backward induction. In period 2, the host and the guests
choose their effort levels. At this stage, the uncertainty on the parameters is resolved, and
thus, the optimization problem of the guest i and the host are given by:
max Ui (ei |eh , ri ) = max{vh + αi u(ei , eh ) − Ci (ei ) + βi ri }
ei
ei
max Uh (eh |ei , rh,i ) = max{vi + αh u(ei , eh ) − Ch (eh ) + βh rh,i },
eh
eh
(12)
(13)
where vh and vi are just exogenous variable and do not affect the optimization problem.
After invoking the truth-telling assumptions, the first order conditions for the two optimality problems are:
e∗i k−1
)
− ci e∗i = 0
e∗h
e∗
(1 − k)(αh + βh βi )( ∗i )k − ch e∗h = 0.
eh,i
k(αi + βi βh )(
13
(14)
(15)
By the optimality conditions, we obtain the following solution for e∗i and e∗h :
e∗i = A(αh + βh αi )γ (αi + βi αh )1−γ
(16)
e∗h = B(αh + βh αi )µ (αi + βi αh )1−µ ,
(17)
where γ ≡ 1−k
and µ ≡ 1 − k2 ; A ≡ ( cki )1−γ ( 1−k
)γ and B ≡ ( cki )1−µ ( 1−k
)µ .
2
ch
ch
Then we have following proposition:
Proposition 1. The host’s average rating on Airbnb positively depends on her weight on
shared experience which we also refer as the weight on reciprocity, i.e., let Rairbnb denote the
´
average rating of the host, Rairbnb ≡ rh,i di, ∀αh > 0
∂Rairbnb
> 0.
∂αh
(18)
Proposition 1 states that, given that the agents report their utility in the feedback, the
average rating of a host reflects her characteristics. Intuitively, a host with higher weight
on shared experience is, on average, more willing to help her guests. Then, by reciprocity,
the guests are willing to exert more efforts towards the host. In turn, the higher effort level
exerted by both sides leads to a higher level of shared experience utility, and therefore to a
higher average rating of the host. Formally, from Equation 16 and 17, we have:
∂e∗h
>0
∂αh
∂e∗i
> 0.
∂αh
(19)
(20)
The above equations show that the equilibrium effort levels of the host and the guest
increase with the host’s weight on reciprocity. In turn, as stated before, these efforts increase
the shared experience utility u(ei , eh ). Finally, the higher levels of u(ei , eh ) is reflected in the
higher rating left by the guest i to the host, which leads to the higher average rating for the
host.
In the next proposition, we show that the bilateral reputation system adopted by Airbnb
reveals the hosts’ hospitality characteristics better than a unilateral reputation system where
the host does not rate the guest, i.e., ri = 0.
´ air
Proposition 2. Rairbnb ≡ i rh,i
di is the host’s average rating on Airbnb (bilateral reputation
´ uni
system ), and Runi ≡ i rh,i di is the host’s average rating on an unilateral reputation system
14
. Then we have
∂Runi
∂Runi
∂Rairbnb
∂Rairbnb
>
> 0 and
>
> 0.
∂αh
∂αh
∂βh
∂βh
(21)
The proposition above shows that ratings on both reputation systems depend positively
on the weight of reciprocity and reputation, αh and βh respectively. However, the host’s
average rating on Airbnb responds more to the weight on reciprocity, while the average
rating on the unilateral review system responds more to the weight on reputation.
airbnb
uni
The former part of the statement, ∂R∂α
> ∂R
> 0, demonstrate the impact of
∂αh
h
reciprocity weight on ratings. The positive relationship between the reciprocity weight and
airbnb
> 0, is established in Proposition 1. Thus, in the following
the bilateral rating, ∂R∂α
h
analyses, we just briefly explain why this positive relation also exists under the unilateral
review system. From the proceeding analyses, we know that, independently of the design
of reputation system, the effort exerted by the host is positively determined by the host
weight on shared experience utility, and that such effort determines the effort level of the
∂e∗
∂e∗
reciprocal guests. This leads to the following property: ∂αhh > 0 and ∂αih > 0. Since the
shared experience utility is positively determined by the efforts, the higher efforts resulted
from higher αh transfers into higher shared experience utility, which is revealed in the higher
uni
average rating of the host, Runi . This provides the high-level idea of why ∂R
> 0.
∂αh
To show that ratings in the bilateral system are more sensitive to the reciprocity weight
than those in the unilateral review system, we decompose the explanation in two steps. First,
we show that for the same pair of host and guest i, the guest i exerts less efforts under the
unilateral system. Second, we demonstrate that, if two hosts only differ in the reciprocity
weight and transact with the same guest i, the higher the guest’s effort is, the larger is the
effort difference between two hosts.
It is easy to see why guests exert more efforts under bilateral system, if we know that
guests on Airbnb also have reputation concerns. In the bilateral system, the host can rate
the guest i, bringing reputation concerns to the guests, thus, the guest i exerts more effort
than under the unilateral review system.
Then we show the positive relation between a guest’s effort and the effort difference
between two hosts by an example. Suppose host Ann has higher reciprocity weight than
host Bob. From the first order condition of the host’s optimal problem, we have that, given
the same level of ei , eAnn (ei ) > eBob (ei ). This means that Ann exerts more efforts than Bob,
if they transact with the same guest. Moreover, αAnn > αBob means that Ann cares more
about reciprocity than Bob. Thus, when guest i increases her effort, Ann is more willing
to reciprocate, i.e., the value of (eAnn (ei ) − eBob (ei )) increases with regard to ei . Since the
15
shared experience utility, u(ei , eh ), depends positively on eh , the larger difference between
eAnn and eBob transfers into a larger difference of the shared experience utility, which is
revealed in the rating difference between Ann and Bob.
Thus, guests exert more efforts on the bilateral than on the unilateral review system,
and this higher level of guest’s effort leads to a larger rating difference between two hosts
who differ only in the reciprocity weights. This means that, given the same set of shared
experience weights, their impact on ratings in a bilateral system are larger than that on the
unilateral review system.
Following a similar reasoning, we can show that the ratings on both systems positively
relate to the host’s weight on reputation, and that the unilateral review system responds
more to the reputation weight, βh .
Given Proposition 2, we hypothesize that the reputation ranking of listings can be different on the bilateral and the unilateral review system. The ranking on the bilateral system
reflects more of the hospitality of the hosts, while the ranking on the unilateral review system reflects more the weight on reputation of the hosts. Moreover, since bilateral system
is more responsive to the reciprocity weight of the hosts, this design of reputation system
makes reciprocity more salient on Airbnb than an unilateral reputation system. This further justifies our assertion that reciprocity has non-negligible role in many sharing economy
platforms adopting bilateral reputation systems, like Airbnb.
The final proposition of our baseline model establishes the positive relationship between
the price and ratings.
Proposition 3. On Airbnb, prices increase after a positive shock on ratings, and decrease
after a negative shock on ratings. Given the same price P1 at period 1, we have the following
0
relationship for prices posted at period 3 and ratings Rairbnb and Rairbnb
disclosed in period
2,
0
0
if Rairbnb > Rairbnb
then P3 (Rairbnb ) > P3 (Rairbnb
).
(22)
Proposition 3 shows that the listing price responds to the rating of the host. This results
from the informativeness of the ratings: a host with higher average rating will look more
attractive to future guests, and therefore will have higher expected demand than another
host with the same price but lower average rating. Since the period 3 price is determined by
the expected demand, the host with higher average rating will increase the price.
The formal proofs of all the propositions discussed so far are reported in Appendix A.
Given the propositions we discussed above, we have the following claims:
Claim 1. The hosts with higher weight on the reciprocity have higher average ratings.
16
Claim 2. For a given set of hosts, the one with higher reciprocity weight and lower reputation
weight is ranked higher on Airbnb than her counterpart with lower reciprocity weight and
higher reputation weight, while the opposite is true on the unilateral reputation system.
4.3
Relaxing the truth-telling assumption
To show the robustness of our main results, we relax the truth-telling assumption, allowing
selection bias and rating inflation, as observed in Fradkin et al. (2015). Now, rating given to
the host, denoted as rh,i , is a choice variable of guests, which means guests do not automatically report their utility in ratings. Instead, they can choose not to disclose rating, disclose
a rating not equal to their utility, or still truthfully report their utility in ratings.
Formally stated, let ωi (ei , eh , vh ) ≡ vh +αh u(ei , eh ) be the total utility that guest i obtains
from the accommodation stay. Let φ denote the mapping from the guest’s utility to ratings,
i.e., φ : Ω → R, where Ω and R are the sets of all possible ωi and all possible rh,i . In this
general setup, not disclosing ratings due to selection bias is modeled as φ(ωi ) = 0, for some
ωi . Meanwhile, when the guests choose what value of rating to report, we allow guests to
inflate ratings, i.e., φ(ωi ) > ωi .
Besides introducing selection biases and rating inflation, this extended model still assume
that guests care about informational value of the ratings when they make rating decisions.
If not, the ratings would loose informational value, contradicting our empirical finding of
rating informativeness. Thus, we assume guests trade-off informational value of rating and
psychological cost of disclosing low rating, when they make rating decisions. To accommodate this trade-off between rating informativeness and psychological reasons, we allow
φ(ωi ) 6= ωi , yet still assuming φ to be a weakly increasing function of ωi . This assumption
means that we do not consider the case where ratings decrease with guest’s utility or the
case where ratings do not respond to the accommodation experience, i.e., φ(ωi ) is a constant
function or decreasing function over ωi
By this extended model, our main result on the rating’s revelation of reciprocity weight
still holds. Formally speaking, since rh,i = φ(ωi ) ≡ φ(vh + u(ei , eh )) and φ is weakly increas´
ing, rh,i still increases with αh . Thus, the average rating of the host, Rairbnb ≡ rh,i di, also
increases with αh . Therefore, even when we allow selection bias and rating inflations, the
ratings reflect, to some degree, the accommodation experience.11 Finally, since the guest’s
accommodation experience is determined by the host’s reciprocity weight, the rating about
the accommodation experience still reveals the host’s reciprocity weight. For a detailed proof
11
For example, one guest may choose not to disclose her rating after a bad experience. However, she does
not rate a bad experience better than a good one. Thus, the rating a guest discloses still weakly reveals the
ranking of her experience.
17
the reader can refer to the Appendix A.2.
5
Empirical analysis
In this section, we empirically test the predictions of our model using consumer-facing information we collected from the Airbnb website.
5.1
Revelation of reciprocity weight in ratings
Proposition 1 states that a hosts’ ratings on Airbnb are positively related to the hosts’
reciprocity weight, αhe . In other words, the proposition claims that because guests report
their utility in their feedback, the average ratings of hosts reflect the host characteristics. A
host that cares more about the reciprocity is more likely to exert more effort eh,i , which in
turn will motivate the guest to increase her effort (because of the reciprocity mechanism).
Finally, increased effort exerted by both parties leads to higher utility, and therefore higher
ratings.
While we do not directly observe how much hosts care about reciprocity, we do observe
variables that are likely to be correlated with the host characteristics. To provide evidence
that such proxies are an indirect measure of the reciprocity weight we show two facts: first,
in line with our theory, we show that these measures are positively correlated with ratings;
second, we show that they are negatively correlated with the amount of time a listing is
available on Airbnb. This second check is important because, as we discussed in Section 3.1,
hosts who participate frequently in the market have lower ratings that those that only occasionally rent out properties. Our model explains this pattern by claiming that professional
hosts have high reputation weight, but low reciprocity weight. Therefore, assuming that our
reciprocity weight proxies are correct, we should observe a negative relationship between
them and the listing availability.
5.1.1
Proxies for reciprocity weight
Host-to-Guest Review length Our first proxy for reciprocity weight is whether the host
writes long reviews about her guests. Intuitively, a host that cares more about the overall
Airbnb experience will take more time to report such an experience in the review. Note that,
because the content of the review (and thus the length) is not disclosed to the guest until
the end of the 14-day review window, this proxy cannot have an impact on guest ratings
(e.g., a good review from the host to the guest cannot incentivize a good review from the
same guest to the host.) Further, the reviews that hosts leave for guests are not displayed
18
on hosts’ Airbnb page, and, therefore, hosts have little incentive to behave strategically with
respect to reviews they leave for guests.
We hypothesize that hosts that leave longer reviews about their guests are more likely
to have higher reciprocity weight, and in turn higher average ratings. Figure 7 plots listing
ratings as a function of the length (in characters) the listings’ owners write for their guests.
We observe a clear positive correlation between host-to-guest review length and listing rating,
which we interpret as evidence in favor of our hypothesis. Further, this relationship holds
when we consider private or shared accommodations (Figure 7).12
Not instant bookable The second proxy we use is whether the host has activated the
instant book feature. Similar to hotel reservations, reservation requests for instantly bookable
Airbnb listings do not require explicit host approval.
We hypothesize that hosts using the Instant Book feature have more weight on the
reputation than on the mutual experience, thus they should have lower ratings than hosts
not using this feature. In Figure 8 we plot the average ratings of listings with and without
the Instant Book feature, by type of accommodation. We observe that for both private and
shared properties, the average ratings are higher for those listings that do not use the instant
book feature, again confirming our hypothesis.
5.1.2
Negative correlation between reciprocity proxies and listing availability
As discussed above, if the proxies described are an indirect measure of the hosts’ reciprocity
weight, they should all be negatively correlated with the availability of their listings. We
test this hypothesis by estimating a straightforward linear regression as follows:
Pct. Availabilityi = β1 log Host-to-Guest Review Lengthi
(23)
+ β2 Not Instant Bookablei + Xi + i ,
where the dependent variable is the availability of listing i and the coefficients of interest
are the variables corresponding to our reciprocity weight proxies. Finally in Xi we include a
set of controls such as the number of reviews received, the average price of the host’s listing,
and the average star-rating.
We report our results in Table 1. In the first column, we present results without including
any controls. The estimated coefficients support our hypothesis: longer reviews and not being
instantly bookable are negatively correlated with listing availability. In column 2, we also
12
The same relationship holds when we consider hosts with one listing or multiple listings.
19
control for the (log of) number of reviews a listing has and the (log of) the listing’s price.
In column 3, we incorporate the listing’s average star rating. In all cases we find a negative
relationship between our reciprocity weight proxies and availability.
5.2
Rating informativeness
Proposition 3 states that hosts are sensitive to changes in reputation. In particular, listing
prices should increase after a positive shock on ratings and decrease after a negative shock
on ratings. To test this proposition, we exploit a unique characteristic of the Airbnb platform: a listing’s average rating is only disclosed after the listing accumulates three reviews.
This provides us with a simple natural experiment to test the hosts’ reaction to the public
revelation their reputation.
A general concern when measuring the impact of ratings on prices is that the that unobserved changes in listing quality can bias our estimates, i.e, listing quality is endogenous since
it is likely to be correlated with both ratings and prices. The following scenario describes
a situation where measuring the impact of ratings on prices will lead to a biased estimate.
Suppose that, at the time at which ratings are made publicly available, the host also makes
an improvement in quality (e.g., upgrades the bed, or installs a new air conditioner.) At
the same time, since the listing’s quality has improved, the host raises the listing’s price. A
simple estimation of the difference in price between the pre-disclosure period and the postdisclosure period will lead to mistakenly attributing the rise in prices to rating disclosure,
when it is in fact driven by changes in quality.
To alleviate the concern of unobserved quality changes, we implement the following identification strategy. We exploit the fact that ratings are a proxy for quality. Therefore, if we
can hold listing quality constant prior to the rating disclosure, we can increase our confidence
in obtaining a consistent estimate the impact of reputation disclosure on prices. While it is
impossible to fully control for listing quality, we can make sure that the ratings up to and
including the third review (when disclosure occurs) do not change. While ratings are not
visible prior to the third review, we know that for a listing to obtain an average of 5 stars
at the time of disclosure, the host must have received three 5-stars reviews (Airbnb rounds
ratings to the nearest half-star, and the only set of three ratings that results in a rounded
5 stars rating is a set of three 5-stars reviews.) Therefore, to implement our identification
strategy we limit our data to the subset of listings for which the disclosed star rating is exactly 5 stars. Moreover, since we are interested in the immediate effect on rating disclosure
on prices, we only consider listing prices up to and including the third review. Therefore,
the treatment effect we estimate is the average difference in prices between the period when
20
listings had between 0 and 2 reviews (the pre-disclosure period), and the period when listings
had exactly 3 reviews (the disclosure period.)
The following model implements our identification strategy:
log Priceit = β Rating Disclosedit
(24)
+ Xit + τt + li + it .
The dependent variable is the log of the price of listing i in week t. Rating disclosedit , whose
coefficient is of interest, is an indicator of whether the average rating of listing i has been
disclosed in week t. In Xit we include a set of time-varying controls to further account for
changes in listing quality such as the number of reviews and the number of photos of the
listing being posted on Airbnb. Further, we include listing (li ) and year-week (τt ) fixed
effects, to control for unobserved time invariant listing characteristics and shocks (to prices)
common across listings, e.g., prices are higher during holiday seasons. Finally, we cluster
standard errors at the listing level.
We present the results of this analysis in Table 2. In the first column of Table 2, we
report the estimate without any controls. The coefficient of interest is positive and highly
significant (p < 0.01), and suggests that rating disclosure leads to a 1.6% increase in the
listing price. In column 2 we add the (log of) number of reviews as a control. The coefficient
of interest is similar in magnitude and significance to the previous one. Finally, we test the
robustness of our results by including a set of time varying observable listing characteristics
for each listing. Specifically, we control the number of pictures associated with the listings,
the type of the listing’s cancellation policy, the number of Airbnb listings in the same ZIP
code, and several observables attributes that can vary over time. We report the estimates
of this specification in column 3 of Table 2. The results obtained are similar to those in
magnitude to those presented in columns 1 and 2.
Overall, the empirical evidence provided in this section is consistent with the predictions
made in our analytical framework: hosts with higher reciprocity weight have higher ratings
than those hosts that place more weight on reputation. Further, prices respond to changes
in ratings, confirming the informativeness of Airbnb ratings.
6
Conclusion
Two salient characteristics of the sharing economy make these marketplaces unique and
interesting to study. First, transactions often involve a social component, i.e., most of the
time buyers and sellers have a close interaction. For example, Uber allows anyone to become
21
a taxi driver, therefore, unacquainted users share the same car for a limited period of time;
similarly, Airbnb allows people to rent out their extra space to anyone in the world, bringing
strangers together under the same roof. Second, because transactions are between peers
rather than firms and customers, sellers have a much lower market power resulting in a
reduction of information asymmetries between the transacting parties.
Because of these features, the behavior of buyers and sellers in these markets is very
different from that observed in more traditional marketplaces. For example on Airbnb, hosts
are encouraged to provide experiences, not “simple stays”.13 Therefore, it is not uncommon
that hosts help travelers learn about hidden gems, the local culture, or fun activities. Airbnb
guests tend to respond to such behavior by behaving better themselves, for example, by
keeping the place clean or respecting the house rules.
In this paper, we take a close look at the sharing economy and its transactions, and
present an analytical framework that, by introducing the concept of reciprocity, describes
how buyers and sellers interact in these markets. We show that reciprocity, the tendency
to increase effort in response to others’ increased effort, perfectly captures the dynamics
of the user interaction and behavior in these markets. We demonstrated that the users’
reciprocal behavior improves their welfare, affects the ratings disclosed and therefore the
market equilibrium. Finally, we test the key predictions of our analytical framework using
data collected from Airbnb, a popular peer-to-peer rental accommodation website.
Our work contributes to the existing literature on the sharing economy, by deepening the
understanding of how trust is generated in the sharing economy. We show that reciprocity
informally regulates players’ behavior and generates cooperation. Moreover, we show that
more reciprocal sellers are rewarded with higher ratings and that bilateral reputation systems,
such as the one implemented by Airbnb, are more responsive to this kind of behavior than
unilateral review systems. Thus, bilateral review systems better serve the purpose of creating
trust among users.
Finally, our work has important implications for market designers. Because our model
shows that reciprocity affects the market equilibrium, matching buyers and sellers, and promoting reciprocal behavior become extremely important. While a good matching mechanism
can induce positive reciprocity which, in turn, increases the welfare of both host and guest,
a bad matching can trigger a negative reciprocity that will worsen the overall experience.
Our work is the first step towards the understanding of user behavior in the sharing
economy, and the first to apply reciprocity theory in the context of these markets.
13
https://www.airbnb.com/experience/signup
22
References
Almlund, Mathilde, Angela Lee Duckworth, James J Heckman, Tim D Kautz. 2011. Personality psychology and economics. Tech. rep., National Bureau of Economic Research.
Charness, Gary, Martin Dufwenberg. 2008. Contracts and communication. American Economic Review .
Ellingsen, Tore, Magnus Johannesson. 2006. Pride and prejudice: The human side of incentive theory .
Fradkin, Andrey, Elena Grewal, Dave Holtz, Matthew Pearson. 2015. Bias and reciprocity
in online reviews: Evidence from field experiments on airbnb. Proceedings of the Sixteenth
ACM Conference on Economics and Computation. ACM, 641–641.
Horton, John, Joseph Golden. 2015. Reputation inflation: Evidence from an online labor
market. Work. Pap., NYU .
Irlenbusch, Bernd, Gabriele K Ruchala. 2008. Relative rewards within team-based compensation. Labour economics 15(2) 141–167.
Kirchler, Erich, Ernst Fehr, Robert Evans. 1996. Social exchange in the labor market: Reciprocity and trust versus egoistic money maximization. Journal of Economic Psychology
17(3) 313–341.
Malmendier, Ulrike, Vera L te Velde, Roberto A Weber. 2014. Rethinking reciprocity. Annu.
Rev. Econ. 6(1) 849–874.
Rabin, Matthew. 1993. Incorporating fairness into game theory and economics. The American economic review 1281–1302.
Sobel, Joel. 2005. Interdependent preferences and reciprocity. Journal of Economic Literature
392–436.
Tadelis, Steven. 2016. Reputation and feedback systems in online platform markets. Annual
Review of Economics 8(1).
Zervas, Georgios, Davide Proserpio, John Byers. 2015a. A first look at online reputation on
airbnb, where every stay is above average. Where Every Stay is Above Average (January
23, 2015) .
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Zervas, Georgios, Davide Proserpio, John W Byers. 2015b. The impact of the sharing economy on the hotel industry: Evidence from airbnb’s entry into the texas market. Proceedings
of the Sixteenth ACM Conference on Economics and Computation. ACM, 637–637.
24
4
59.5%
3
Density
# of listings
30000
20000
32.3%
2
10000
1
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1.5%
0
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Pct. availability
Figure 1: Listing star-rating distribution.
Figure 2: Probability density function the
listing availability.
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Pct. availability
Figure 3: Listing star-rating as a function of listing availability. The blue line represent the
linear fit (over the real data) and the grey shade its standard error.
25
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Figure 4: Listing star-rating as a function of listing availability broken down by hosts with
1 listing and 2+ listings. The blue line represent the linear fit (over the real data) and the
grey shade its standard error.
Shared accommodation
Private accommodation
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Figure 5: Listing star-rating as a function of listing availability broken down by the listing
type: private accommodation (entire house/apartment) and shared accommodation (private
or shared room). The blue line represent the linear fit (over the real data) and the grey
shade its standard error.
26
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Figure 6: Average listing star-rating as a function of the host-to-guest review length. The
blue line represent the linear fit (over the real data) and the grey shade its standard error.
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Figure 7: Average listing star-rating as a function of the host-to-guest review length. broken
down by the listing type: private accommodation (entire house/apartment) and shared accommodation (private or shared room). The blue line represent the linear fit (over the real
data) and the grey shade its standard error.
27
Shared accommodation
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Not instant
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bookable
Figure 8: Average listing star-rating as a function of whether the listings have activated
the Instant Book feature broken down by listing type: private accommodation (entire
house/apartment) and shared accommodation (private or shared room).
28
Table 1: Correlation between listing availability and reciprocity weight proxies.
log Host-to-Guest Review Length
Not Instant Bookable
(1)
(2)
(3)
(4)
−0.006***
(−3.00)
−0.016***
(−7.69)
−0.015***
(−7.07)
−0.009***
(−3.82)
−0.063***
(−19.65)
−0.043***
(−13.54)
−0.041***
(−13.03)
−0.031***
(−9.87)
0.068***
(59.35)
0.063***
(54.07)
0.057***
(40.60)
−0.037***
(−20.78)
−0.030***
(−16.09)
log Reviews
log Price
−0.041***
(−10.95)
Star Rating
N
R2 adj.
52966
0.0068
52966
0.066
52966
0.074
41604
0.051
Note: The dependent variable is the percentage of availability of listing i. In column 3 the number of observations
decreases because Airbnb does not provide ratings for listings with less than three reviews.
Significance levels: * p<0.1, ** p<0.05, *** p<0.01.
29
Table 2: The impact of ratings disclosure on listing price
Rating Disclosed
(1)
(2)
(3)
0.016***
(11.80)
0.016***
(11.04)
0.016***
(10.93)
log Reviews
0.000
(0.11)
0.002
(1.12)
log Pictures
−0.009*
(−1.95)
log Extra Guest Price
−0.005***
(−3.08)
Cancellation policy (ref. Flexible)
−0.015***
(−2.81)
Moderate
Strict
0.004
(0.61)
Super Strict
0.007
(0.48)
Super Strict 30-day
0.025
(1.49)
Super Strict 60-day
0.011
(0.56)
Bed type (ref. Airbed)
Couch
−0.071
(−0.97)
Futon
−0.025
(−0.51)
Pull-out Sofa
−0.019
(−0.45)
Real Bed
0.044
(1.64)
Number of Guests Included
0.009***
(2.72)
−0.021***
(−6.16)
Is Instant Bookable
log Min Reservation Nights
0.010*
(1.67)
log Security Deposit
0.003**
(2.35)
log Airbnb Zipcode Supply
0.002
(0.44)
N
R2 within
352281
0.0044
352281
0.0044
352281
0.0095
Note: The dependent variable is the (log) price of listing i at time t. All the modesl include year-week and listing fixed effects. Cluster-robust t-statistics (at the individual
listing level) are shown in parentheses.
Significance levels: * p<0.1, ** p<0.05, *** p<0.01.
30
A
Mathematical Appendix
A.1
A Simple model
We start with a simple model where we assume the host to be a risk-neutral profit maximizer.
The service quality offered by the host is exogenously given and fixed across transactions.
Further, the service quality is private information of the host and only revealed to the guests
during their stay in the host’s property. The distribution of service quality is common
knowledge. We assume a monopoly host and a continuum of guests with heterogeneous
tastes. The guests are located on a line where the host is located at the center. The
heterogeneous taste of guest i is modeled as xi , which denotes the distance between the host
and the guest i, and it follows a uniform distribution over [0, 1]. Without loss of generality, we
assume the effort cost of publishing a review is zero. The time framework of the benchmark
model is as follows:
• At period 1, the host post price P1 and a continuum of guests – the early guests –
enter the market. The early guests can only observe P1 and the expected value of
service quality, E(vh ). Guests decide whether to request accommodation and hence
the transaction volume for this set of guests, Q1 , is realized.
• At period 2, the accommodation stay takes place. The guest who requests the accommodation now knows the true value of service quality and realize her utility vh − xi .
At the end of this period, the guest i also publishes a rating rh,i for the host.
• At period 3, the host observes the ratings received in period 2 and post a new price P3 .
A continuum of guests – the late guests – enter the market. Their heterogeneous taste
xi follows the same distribution of the early guests. They observe the average rating
of the host disclosed at period 2 and the price P3 . They make their accommodation
decision accordingly.
As argued before, under this scenario, a rational agent does not have any incentive to lie
in her ratings. Therefore, since the truth-telling ratings have positive externality to other
users on the platform, we assume the guests always tell the truth and report their utility
in their ratings, i.e., rh,i = vh − xi , where vh denotes the service quality and xi denotes the
heterogeneous taste of guest i.14 Moreover, we assume that the distribution of vh and xi is
common knowledge and, hence, E(vh ) is known ex-ante to the guests and E(xi ) is known
ex-ante to the host.
14
Note that, since P1 is common knowledge, assuming rh,i = vh − xi or rh,i = vh − xi − P1 is exactly the
same for our analysis.
31
In this setting, the only choice variable of the host is to determine the price by maximizing
her profit. The objective function of the host is given by
Vh (P ) = max{E[P Q − C(Q)|P ]
P
(25)
where P denotes price and Q denotes the transaction volume. Vh (P ) denotes the ex-ante
utility contingent on choosing price P . Since the host is risk-neutral and only interested in
expected profits, the utility function coincides with the expected profits.
Similarly, the only choice variable of a guest is to determine whether to request accommodation. A guest requests accommodation from the host if and only if her expected utility
from the accommodation is non-negative. The guest’s ex-ante utility prior to the accommodation is given by
Vi (transact|P ) = E(vh ) − xi − P
(26)
where Vi (transact|P ) is the ex-ante utility of the guest i if she books the accommodation.
P denotes the price set by the host, vh denotes the service quality, and xi denotes the
heterogeneous taste of guest i.
After staying in the host’s property, the guest i publishes a rating rh,i = vh − xi . The
´
average rating R ≡ rh,i di depends solely on vh and E[v(h)].
In the solution below, we solve backward for Perfect Bayesian Equilibrium.
Proof : In the first period, early guests make a decision based on E(vh ). The distribution
of vh is common knowledge, so is E(vh ). When the host chooses P1 , the marginal guest i∗
who is indifferent about reserving the accommodation or not, is given by
E(vh ) − xi∗ − P1 = 0.
(27)
Guests with x ∈ [0, xi∗ ] book the accommodation. Hence, the first period transaction volume
is
Q1 = xi∗ = E(vh ) − P1 .
(28)
Now let’s consider the distribution of ratings. Since the rating rh,i is given by vh − xi ,
the average rating, denoted as R, is given by
´ Q1
R≡
0
vh − xi dxi
Q1
= vh −
.
Q1
2
(29)
Since both R and Q1 are common knowledge at Period 3, the late guests can infer the value
of vh from vh = R + Q21 . Therefore, at Period 3, the guests have complete information and
32
the marginal guest at Period 3 is given by vh − xj ∗ − P3 = 0, i.e.,
Q3 = xj ∗ = vh − P3 .
(30)
Hence, the host maximizes the profits at Period 3 by solving the following optimality problem
max P3 Q3 = max[P3 (vh − P3 )].
P3
P3
(31)
From the first order condition, we have P3∗ = v2h . Then at Period 1, let’s assume the
hosts discount future revenue at the rate β, the host solves
max[P1 (E(vh ) − P1 ) + βP3∗ (vh − P3∗ )].
P1
(32)
From first order conditions (denoted as FOC thereafter), we have
P1 =
E(vh )
2
(33)
Then from Equations 33 and 28, we have Q1 = E(v2 h ) .
Thus, we have
E(vh )
Q1
= vh −
.
(34)
R = vh −
2
4
For a pool of hosts with vh ∈ [v h , v̄h ], the average value of vh is E(vh ), hence, the average
´
ratings of hosts is M = Rj dj = 43 E(vh ).
Let Rc denote the rating of casual host listings and Rp denote the rating of professional
host listings (thereafter, the subscripts c and p correspond to casual hosts and professional
host, respectively). Thus, to have Rc systematically higher than Rp , we have to assume that
E(vhc ) > E(vhp ), where E(vhc ) and E(vhp ) denote the average service quality of casual hosts
and of professional hosts, respectively. However, the listing availability which distinguishes
the two types of hosts is only a proxy for the market participation frequency of the hosts
and the two groups of hosts mainly differ in the extent of which they care about reputation,
thus we argue that it is not intuitive to assume the listing availability affect exogenously
given service quality.
Simply stated, this model cannot easily explain the systematic difference in ratings because the reputation weight cannot affect the value of E(vh ).
33
A.2
Relaxing the truth-telling assumption
In the next attempt to explain the facts observed, we relax the truth-telling assumption.
Doing so, we allow selection bias in the ratings, as observed in Fradkin et al. (2015).
To accommodate for the selection bias, we assume that the guests provide a rating to a
host only if the rating is above a threshold θi , i.e.,
1{rating} = 1 if f rh,i > θi
(35)
Then the objective function of the guest i is given by
Vi (transact|P ) = E(vh ) − xi − P + E(ri − 1{rating}αi |(vh − xi ) − rh,i |),
(36)
where rh,i denotes the rating guest i gives to the host, and ri denotes the rating the host
gives to the guest i. The term αi denotes the weight of host’s reputation in guest i’s utility.
The rest of parameters and variables are as in the previous model.
Compared with the guest’s ex-post utility in the simple model (Equation 26), the current
utility function has two new parts. The first part includes 1{rating}|(vh − xi ) − rh,i | and
the rating threshold θi . The difference between the disclosed rating and the true level of the
guest’s utility captures the guest’s disutility derived from reducing the rating informational
value. The term θi captures the psychological cost for the guests to give a low rating to the
host. Together, these terms capture the trade-off faced by the guest when choosing whether
to rate the host and what’s the value of rating to disclose.
The second part is ri , the rating guest i receives from the host, which captures the fact
that the guest i has reputation concerns. The reason for ri to be part of the guest’s utility
is to match the realistic setting on Airbnb, where the host can rate the guest, and this
rating affects whether other hosts accept the guest’s future request of accommodation. Note
that, since in all our analyses we restrict the ratings sample to be under the new Airbnb
reputation mechanisms, strategic rating manipulation is not a possibility, i.e., ri does not
affect the rh,i . Therefore, the rating biases come from psychological reasons discussed in
previous paragraph.
In the equilibrium of this model, the host receives a higher rating than in the simple
model, and the inflation of ratings depends on the average level of θi associated with the
pool of the guests. While θi may be affected by the interaction between guests and hosts, it
seems very unlikely that it’s also correlated with the amount of time the listing is available
on the platform, since the availability information is not public knowledge to guests. Unless
one is willing to believe that such correlation exists, we cannot easily explain the difference
34
in ratings observed in Section 3.1. The formal proof of this statement is as follows.
Proof : Under this model, the only choice variable of the guest during period 2 is rh,i . If
guest i decides to request the accommodation, her ex-ante utility at period 1 is given by
Vi (transact|P )
max E(vh ) − xi − P + E[ri − αi 1{rating}|rh,i − (vh − xi )| (37)
=
rh,i
1{rating} = 1 if f rh,i > θi .
where
The ex-post utility of guest i at the end of Period 2 is given by
ui (rh,i )
max[vh − xi + ri − αi 1{rating}|rh,i − (vh − xi )]|
=
rh,i
where
(38)
1{rating} = 1 if f rh,i > θi .
With respect to the best response of guest i, two options exist:
1. If rh,i > θi , then:
Vi (transact|P ) = E(vh ) − xi − P + E[ri − αi |rh,i − (vh − xi )|
(39)
ui (rh,i ) = [vh − xi + ri − αi |rh,i − (vh − xi )]|
(40)
where ui (rh,i ) is the ex-post utility after the accommodation stay.
Then from Equation 40 and αi > 0, we have:
rh,i = vh − xi .
(41)
2. If rh,i ≤ θi , then, the guest i does not give any rating. Thus, ui = vh − xi + ri .
Then the ex-ante utility for a guest to enter the market is given by:
Vi (transact|P ) = E(vh ) − xi − P + E(ri ) + αi [P rob(vh − xi > θi ) ∗ 0
(42)
+ (1 − P rob(vh − xi > θi )) ∗ 0]
Note that under simultaneous ratings, guest i cannot have any influence on ri . Thus,
the decision rule of guest i at period 1 is exactly the same discussed in the simple model:
transact if and only if E(vh ) − xi − P ≥ 0. Therefore, the following conditions still hold:
Q1 = x∗i = E(vh ) − P1 and P1 = E(v2 h ) .
35
Then the average rating of a host under this model, denoted as Rbiased , is:
R
biased
´
´
r di
(v − xi )di
i´rate h,i
´ h
≡
= i rate
1di
1di
i rate
i rate
´
x df (xi )
´ i
= vh − i rate
di
i rate
´ x∗∗
xi df (xi )
= vh − ´0 x∗∗
df (xi )
0
where x∗∗ ≡ min{vh − θi , E(vh ) − P1 }, and f is the density function of xi .
Then, denoting the average rating in the simple model as Runbiased ≡
that
Rbiased − Runbiased = g(θ) > 0
´
i´rh,i di
i
idi
, we have
(43)
i.e., the average rating under selection bias is higher than the average rating without selection
bias, and their difference is a function of θ. Under such condition, to observe systematically
low ratings for professional hosts we need to assume that vhp is systematically lower than vhc ,
or that the distribution of vhc First Order Stochastic Dominates (FOSD) the distribution of
vhp .
Another alternative to explain the rating patterns observed, is to assume that guests
of professional and casual hosts differ systematically in their θ, the psychological cost of
leaving a bad review. Specifically, guests of professional hosts must have a systematically
lower psychological threshold than guests of casual hosts. However, guests cannot observe
hosts availability and, thus, they cannot discern between professional or casual hosts; and
hosts cannot infer the guests’ θ, so they cannot select a specific type of guest. Thus, this
self-selection of guests depending on the host type (or vice versa) is unlikely to occur in
reality.15
A.3
Relaxing the risk neutral assumption
In this section, we relax the risk-neutral hosts assumption, and allow the behavior of the
guests to enter into the utility function of the host. We propose this modification because
of the nature of Airbnb transactions. Since Airbnb hosts share their own properties, it’s
natural to expect them to be risk adverse towards the misconduct of the guests.
15
Note that even under the assumption that hosts are able to infer the guests’ θ, all hosts, and in particular
professional hosts, who have a higher weight on reputation, would select those guests with higher θ in order
to reduce the probability of receiving a lower rating.
36
Formally speaking, we assume the behavior of the guest i, denoted as ei , to enter into
the utility of the host, and the host’s utility is assumed to be concave with respect to ei .
The utility function of the host is given by:
Vh (P ) = max{E[P Q − C(Q)|P ] + E[(rh,i + uh (ei ))|P ]}
P
(44)
where, as before, P denotes price, Q denotes the transaction volume, and vh (P ) denotes
the ex-ante utility contingent on choosing price P . rh,i is the rating the host receives from
the guest i. The term uh (ei ) shows that the guest’s effort ei affects the host’s welfare. The
concavity of uh captures the risk aversion of the host. Then, the host trade-off the expected
profit with the possible misconduct of the guests to determine how many guests she wants
to get. While the introduction of this assumption reduces the number of guests the host will
accept, the host’s ratings do not alter the service quality, since it is exogenously given and
fixed. Formally, the only choice variable is still P and the optimality problem of the host is
reduced to:
max{E[P Q − C(Q)|P ] + E[(rh,i ]}.
(45)
P
Independently of which assumptions are invoked on the rh,i , the absence of strategic manipulation on rh,i makes it impossible to alter the optimality problem, which therefore is
analogue to the benchmark case.
Moreover, since the service quality is exogenously given in this scenario, to reconcile the
facts observed we still need to assume that the service quality of casual and professional
hosts follow different distributions, and that the distribution of vhc FOSD the distribution of
vhp .
A.4
Endogenize service quality
Here, we relax the exogenous service quality assumption. We allow the service quality to
vary among different transactions with different guests. This assumption is consistent with
the high heterogeneity and high volatility of the service quality on Airbnb. In this attempt,
we consider three alternative models.
A.4.1
Model I - Host only cares about profit and reputation
First, we endogenize the service quality without changing the assumption that host cares
only about profit and reputation. The optimality problem of the host at Period 1 is given
by:
Uh,1 (P ) = max{E[P Q − C(Q)|P ] + E[Uh,2 (eh , rh,i )]}.
(46)
P
37
As argued in Section 3, the demand is realized at Period 1 while only the reputation
concerns and effort cost determine the effort level at Period 2. Then, the host’s optimality
problem at Period 2 is given by:
Uh,2 (eh , rh,i ) = max{βh rh,i − Ch (eh )}.
eh
(47)
With higher market participation frequency, the professional hosts have higher weight
on reputation concerns, i.e., professional hosts have systematically higher βh . With the
assumption that guests report their utility in ratings rh,i , we can assume rh,i = eh .
From the First Order Conditions, we have
Ch0 (eh )∗ = βh .
(48)
The above condition solves the optimal level of e∗h .
If the effort cost function is identical across hosts, i.e., the function Cp (eh ) = Cc (eh ) for
all eh , then the professional hosts exert higher level of efforts due to their higher βh , i.e.,
from βp > βc and Ch0 ≥ 0, e∗p > e∗c .
Even if the effort cost function of professional hosts is systematically different from that
of casual hosts, because of economic of scale, it is unlikely that the latter have systematically
lower marginal effort cost than the professional hosts. That is, C 0 (ep ) ≤ C 0 (ec ) for each given
eh . Even if we assume C 0 (ep ) > C 0 (ec ) for some eh , the difference in marginal effort cost
has to be large enough to offset the effect of βh so that the non-professional hosts can exert
systematically higher effort under this model. Therefore, this model cannot easily reconciles
the facts observed.
A.4.2
Model II - Host also cares about guest behavior
In this model hosts also care about the guests behavior. As argued above, the hosts on Airbnb
are relatively “small” service providers compared to firms in the accommodation industry,e.g.,
Hilton Hotels. Therefore, a natural assumption to introduce is that hosts are also risk-averse
utility maximizers, and that the guests conduct enters into their utility function. However,
we show in later proof that only introducing guests conduct enter a risk-averse host’s utility
does not suffice to reconcile the fact. Formally speaking, if we assume ei and eh are separable
in host’s utility, guest’s behavior cannot alter the host’s effort. Thus, we have to further
assume a non-separable function of eh and ei in our main model, the model of reciprocity.
With a separable functional form of ei and eh of Uh , the optimality problem of the host
38
is given by:
Uh (eh , rh,i ) = max g(ei ) − Ch (eh ) + βh rh,i
eh
(49)
where g(ei ) captures the effect of guests’ conduct on the host’s welfare, and the concavity of
g(·) models the host’s risk averse attitude towards the guests’ behavior.
Assuming rh,i = eh , we have the same first order condition as the previous model, i.e.,
0
Ch (eh )∗ = βh . This means that ei does not determine the optimal level of eh and therefore
it cannot alter the qualitative result of the previous model.
A.4.3
Model III - Host has interdependent preference.
In the following analysis, we assume the host has interdependent preference (without assuming the reciprocity feature discussed in our main theoretical framework), i.e., the utility of
guest i, denoted as Ui , enters into the host’s utility function.
Under this assumption, the optimality problem of the host is given by:
Uh (eh , ei , rh,i ) = max g(ei ) + Ui (ei ) − Ch (eh ) + βh rh,i
eh
(50)
where Ui is the ex-post utility of the guest i and is given by Ui (ei , eh , ri ) = f (eh )−Ci (ei )+βi ri .
Also, ei and eh are the efforts of the guest i and the host, respectively. The g(·) denotes how
much the host care about the guest’s behavior, and f (·) is the impact of the host’s effort on
the guest’s utility.
To derive a close-from solution of the optimal effort level, we assume f and g to be
f (eh ) = eh1−k and g(ei ) = eki , and the effort cost function to be quadratic, i.e., C(eh ) = c2h e2h .
16
After invoking ri = g(ei ), rh,i = f (eh ), we have:
(1 + βh )f 0 (eh ) = Ch0 (eh )
1
(51)
∂e∗
h ) k+1
)
and ∂βhh > 0.
Then, we have e∗h = ( (1−k)(1+β
ch
If the casual hosts differ from the professional hosts only by βh , and the professional hosts
p
c
have higher level of βh , we have e∗p > e∗c . Therefore, rh,i
< rh,i
, ∀i. Thus, the average rating
of the professional hosts are expected to be higher than those of casual hosts, contradicting
the empirical facts.
In order to match the systematically lower ratings for the professional hosts, this model
needs an extra assumption. Specifically, we need to assume that the casual hosts are sys-
16
Note that the following results does not rely on assuming f and g to be of a specific form. A quadratic
effort cost function and increasing f and g suffice for our results to hold.
39
tematically more altruistic than their counterpart. This assumption can be implemented
by adding the parameters αg in front of the interdependent utility term in the gross utility
of the host, and assuming that the difference on the altruism weights are larger than the
difference between reputation weights. Formally stated:
αcg − αpg > βp − βc > 0,
where αcg and αpg are the weight on the guests’ utility of the non-professional hosts and the
professional hosts, respectively.
By invoking this assumption, we allow the casual hosts to have systematically higher
intrinsic altruism towards the guests, and the difference between altruistic attitude is large
enough to offset the difference between reputation concerns. However, we consider altruistic
behavior a larger departure from standard assumptions, and a worse fit to explain Airbnb
users behavior than our reciprocity model.
A.5
A.5.1
Reciprocity model
Proof of proposition 1
Proposition 1. The host’s average rating on Airbnb is positively related to her weight on
mutual experience utility, i.e., ∀αi ≥ 0 and αi =
6 0,
∂Rairbnb
>0
∂αh
(52)
ˆ
where
Rairbnb ≡
rh,i (eh , ei )di
(53)
i
is the average rating of the host.
Proof : We solve the subgame equilibrium at Period 2. Note that at Period 2, both
players choose their optimal effort level as best response to the other’s effort. Then each
player reports their utility of accommodation in the rating.
Plugging rh,i (ei , eh ) = vi (ei , eh ) and ri (ei , eh ) = vh (ei , eh ) into the ex-post utility of host
and guest i, we have
Ui (ei |eh ) = max[vi (ei , eh ) − P − C(ei ) + βi vh (ei , eh )]
(54)
Uh (eh |ei ) = max[vh (ei , eh ) − C(eh ) + βh vi (ei , eh )]
(55)
ei
eh
40
Combining the first order conditions of the two optimality problems, we have
e∗i = A(αh + βh αi )
1−k
2
(αi + βi αh )
k
1+k
2
k
e∗h = B(αh + βh αi )1− 2 (αi + βi αh ) 2
1−k
1+k
k
k
where A ≡ ( cki ) 2 ( 1−k
) 2 and B ≡ ( cki )1− 2 ( 1−k
)2
ch
ch
1+k
1−k
k 1−k
Thus, rh,i (ei, eh ) = vh + αi ei eh = vh + αi [A(αh + βh αi ) 2 (αi + βi αh ) 2 ]k [B(αh +
k
k
βh αi )1− 2 (αi + βi αh ) 2 ]1−k .
From the above, we have
∂rh,i
>0
∂αh
´
airbnb
Rairbnb ≡ rh,i di and hence, ∂R∂α
> 0.
h
A.5.2
Proof of proposition 2
Proposition 4.2. The ratings on both review systems depend positively on the weights of
reciprocity and reputation, αh and βh . However, the seller’s average rating on Airbnb responds more to the weight on mutual experience utility, and the seller’s average rating on
the unilateral review system responds more to the weight on reputation, i.e,
∂Rairbnb
∂Runi
∂Runi
∂Rairbnb
>
> 0 and
>
> 0.
∂αh
∂αh
∂βh
∂βh
(56)
´ air
´ uni
where Rairbnb ≡ i rh,i
(eh , ei )di is the seller’s average rating on Airbnb, and Runi ≡ i rh,i
(eh , ei )di
is the seller’s average rating on an unilateral review system.
Proof : From proceeding results, we have
e∗i = A(αh + βh αi )
1−k
2
(αi + βi αh )
k
1+k
2
k
e∗h = B(αh + βh αi )1− 2 (αi + βi αh ) 2
For the same host of a property on both the unilateral review system platform and Airbnb,
and given identical values of the parameters, except βi = 0 under the unilateral review
system, we have
air
uni
∂rh,i
∂rh,i
>
>0
∂αh
∂αh
(57)
air
uni
∂rh,i
∂rh,i
<
∂βh
∂βh
(58)
0<
41
Since Rairbnb ≡
´
rair (eh , ei )di and Runi ≡
i h,i
´
runi (eh , ei )di,
i h,i
we have
∂Runi
∂Runi
∂Rairbnb
∂Rairbnb
>
> 0 and
>
> 0.
∂αh
∂αh
∂βh
∂βh
(59)
Thus, under the unilateral review system platform, the hosts that cares more about the
reputation are ranked higher than the hosts that cares more about mutual experience; while
the opposite is true on Airbnb.
A.5.3
Proof of proposition 3
Proposition 3. On Airbnb, prices increase after a positive shock on ratings, and decrease
after a negative shock on ratings. Given the same price P1 at period 1, and ratings Rairbnb
and R̃airbnb disclosed at period 2, we have the following relationship for prices posted at period
3,
if Rairbnb > R̃airbnb then P3 (Rairbnb ) > P3 (R̃airbnb ).
(60)
Proof : Ex-ante, the guests determine whether to enter the market according to Vi (P ).
Guest i enters the market if and only if Vi (P ) ≥ 0, given P . Therefore, the marginal guest
is guest i∗ where Vi∗ (P ) = 0. For each guest i at period 3, the expected utility Vi (P ) is
positively determined by her inference of αh , βh .
From proceeding results, we have
vi + αh u(ei , eh ), we have
∂u(ei ,eh )
∂αh
> 0 and
∂u(ei ,eh )
∂βh
> 0. Together with ri =
∂ri
>0
∂αh
(61)
∂ri
>0
∂βh
(62)
Then, since Ui (ei , eh , ri , vh ) = vh + αi u(ei , eh ) + βi ri , we have: ∀(αi , βi ) > 0,
∂Ui (ei , eh , ri , vh )
>0
∂αh
(63)
∂Ui (ei , eh , ri , vh )
>0
∂βh
(64)
where u(ei , eh ) is the mutual experience utility and Ui (ei , eh , ri ) is ex-post utility of guest i
during the accommodation stay.
At period 3, Vi (P3 ) is the ex-ante utility of the guest i if she decides to transact with the
42
host. The guest i forms her expectation based on the publicly observed price, P3 , and the
´
average rating of the host, Rh ≡ rh,j dj, i.e.,
ˆ
Vi (P ) =
Ui (ei , eh , ri , vh )dF updated (Ψh ),
(65)
where F updated (Ψh ) is the posterior distribution of the host’s characteristic parameter vector
(αh , βh , vh ). The Bayesian-updated guests update the prior distribution F (Ψh ) upon the
signal Rh .
From Equations 63, 64, and 65, we have that ∀(αh , βh , vh ) ∈ Ψh , the expected value of
Ui (ei , eh , ri , vh ) are positively related to αh and βh , i.e.,
∂Vi (P3 )
>0
∂αh
(66)
∂Vi (P3 )
>0
∂βh
(67)
The two conditions above imply that the ex-ante utility to transact is higher, if the host is
perceived to have higher weight on mutual experience or reputation.
Meanwhile, from proceeding results we have
∂rh,i
>0
∂αh
(68)
∂rh,i
>0
∂βh
(69)
Conditions 68 and 69 show that the hosts with higher value of αh and βh have higher
´
rating rh,i given the same guest i. Then, from Rh ≡ rh,i di, we have that, given the same
guests pool, the average rating, Rh , reveals higher value of (αh , βh ).
Suppose that two hosts are identical, except for their ratings.They have the same price
0
P1 , same location, and similar property, but Rairbnb > Rairbnb
. Then the higher rating Rairbnb
0
is a positive signal relative to Rairbnb , i.e., the expected value of the host’s characteristics
is better for the host with Rairbnb . Thus, if the two hosts post identical P3 , the expected
demand towards the host with higher average ratings would be higher, i.e., Q(P3 , Rairbnb ) >
0
Q(P3 , Rairbnb
).
Since each period-3-guest is more willing to transact with the host having Rairbnb than
0
with that having Rairbnb
, the host with higher rating posts higher price P3 (assuming that
the hosts are faced with the same pool of guests).
Formally, let’s suppose P1 and Q1 are the same for Host A and Host B, and without
43
loss of generality, let’s assume the mass of guests enter the market have the same set of
parameters, (αi , βi ). Let the Host A have an average rating Rairbnb and Host B an average
0
0
, then from equation 61 and equation 62, we have at least
. If Rairbnb > Rairbnb
rating Rairbnb
one of the following conditions hold
αA > αB
βA > βB
Then, for any positive P3 ,
Vi (transact with A|P3 ) > Vi (transact with B|P3 )
(70)
The marginal guest is defined as the one with Vi (transact|P3 , Rairbnb ) = 0. Then, from
equation 70, we know that the marginal guest transacting with Host A can bear a higher P3
compared to that trading with Host B, since Host A is expected to have higher value of α
or β or both.
Since P3 is determined by
ˆ
max{P3 Q(P3 ) +
Uh (ei , eh , vh , rh,i )dF (Ψg )},
P3
(71)
0
then we have that, given that Ψg is the same for Host A and B, P3 (Rairbnb ) > P3 (Rairbnb
).
A.6
Relaxing the truth-telling assumption
As defined in Section 4.3, we have that
rh,i ≡ φi (vh + u(ei , eh ))
Plugging the equation above into Rairbnb ≡
´
(72)
rh,i di we have
ˆ
Rairbnb =
φi (vh + u(ei , eh ))di
(73)
Now, assume all hosts are faced with an identical pool of guests. Let ωi ≡ vh + u(ei , eh ).
From proceeding results we have:
∂ωi
>0
(74)
∂αh
44
Since φ is a weakly increasing mapping, we have
∂φ(Ωi )
≥0
∂ωi
(75)
The inequality is strict for some ωi .
i)
≥ 0 and the inequality is strict for some
From the Equations 75 and 74, we have ∂φ(Ω
∂αh
ωi , i.e.,
∂rh,i
>0
(76)
∂αh
45