Reputation Leaders and Quality Laggards: The Incentive Structure in Markets with Both Private and Collective Reputations MARCO COSTANIGRO*, CRAIG A. BOND** AND JILL J. MCCLUSKEY***
Affiliations:
*
Costanigro (contact author): Assistant Professor, Department of Agricultural and
Resource Economics, Colorado State University, B326 Clark Bldg, Fort Collins, CO
80523-1172, telephone 970-491-6948, fax 970-491-2067.
[email protected]
**
Bond: Assistant Professor, Department of Agricultural and Resource Economics,
Colorado State University, B11 Clark Bldg., Fort Collins, CO 80523-1172, telephone
970-491-6951, fax 970-491-2067.
***
McCluskey: Professor, School of Economic Sciences, Washington State University,
101 Hulbert Hall, Pullman, WA 99164-6210; telephone 509-335-2835; fax 509-3351173.
1
Reputation Leaders and Quality Laggards: the Incentive Structure in Markets with Both Private and Collective Reputations Abstract
A theoretical model is developed to illustrate the economic incentives to invest in quality
in markets where reputations are both private and collective. Numerical dynamic
programming techniques are then used to simulate firms’ strategic behavior, showing
how firms with the same production technology may produce above or below the shared
regional reputation. Competitive outcomes are then compared to the optimal investment
strategy of a regional planner (cartel). We find that the competitive/optimal quality ratio
is smaller in the presence of a reputation leader, and regulators wishing to increase
quality should first alleviate asymmetric information, and then target producers’ freeriding behavior.
Keywords: Information and Product Quality, Private Reputation, Collective Reputation
2
Introduction
In markets where consumers face some degree of uncertainty regarding product quality
until after consumption, reputations play an important role. 1 Product, firm, regional
names (such as geographical indications), or other similar signals are often (imperfectly)
associated by consumers with quality outcomes. Realizing that names and reputations
can be private or collective in nature, an extensive theoretical and empirical literature has
been developed on product, brand, regional and franchise reputations (e.g. Klein and
Leffler 1981, Shapiro 1982, Kreps and Wilson 1982, Jarrell and Peltzman 1985, Gale and
Rosenthal 1994, Barber and Darrough 1996, Tadelis 1999 and 2003 for private; Blair and
Kaserman 1994, Tirole 1996, Winfree and McCluskey 2005 for collective).
Even though most of the literature focuses on either private or collective
reputations, in many instances they are coexistent. In addition to private brand
reputation, products such as Japanese cars, Italian shoes, and Swiss watches (or banks)
also share a collective one. Agricultural products pairing brand names and certified
indications of origin (e.g. Roquefort cheese, Scotch whiskeys, prosciutto di Parma) are
common. In the wine industry, each winery has its own brand name(s), yet the region of
production is so important that retailers often display their wine offerings by country and
region of origin to facilitate consumer choice.
Few studies have examined the impact of private and collective reputation
indicators on firms’ investment in quality. Landon and Smith (1998) studied the market
for Bordeaux wines to show that models including proxies for firm reputation (past
quality scores in specialized magazines) and collective reputations (region-specific
intercept shifters) are more predictive than private-only or collective-only models. In a
related paper, Costanigro McCluskey and Goemans (2010) highlighted how names and
reputations nest within each other to identify producers with increasing specificity. They
found that reputation premia for good names tend to migrate from collective to specific
(private) names as product prices increase, mainly because the greater “cost of being
wrong” (and buy poor quality at high prices) justifies the extra search cost necessary to
switch from using few aggregate names to many specific ones. In a recent article,
1
These products are generally referred to as experience goods, following Nelson (1970).
3
Menapace and Moschini (2010) extended Shapiro’s (1983) study on private reputations
to analyze the case in which collective reputations associated with geographical
indications (GI) are used in addition to private names associated with trademarks. Their
principal result is that when GIs impose minimum quality standards (and consumers are
aware of them)2, the cost of establishing reputations for high quality diminishes and so
does the premium consumers need to pay.
The debate regarding the proper use and legislation regarding GIs is ongoing, but,
as Josling (2006) puts it, it is clear that GIs are here to stay. Indeed, GIs are becoming
common in “new world” countries (North America, South America, Australia) outside of
Europe, and markets with dual (private-collective) reputation structure are becoming
increasingly common. It is therefore relevant to investigate whether the economic
incentives associated with private and collective reputations can be studied independently
of each other (as it is done in the existing literature), or some significant interaction arise
when the reputation structure is dual.
In this article, we study producers’ incentives to invest in quality when firms
having their own private brand name also share a common name and reputation. To do
so, we simulate a dynamic game in which profit-maximizing firms invest in quality to
maximize their returns from private and collective reputations. Model parameters are
calibrated using data from the California wine industry, thereby tying the simulation to an
experience good market3. The primary objectives are twofold: 1) to study how the (intraregional) quality-reputation dynamics may differ from markets where reputations are
either exclusively private or collective and 2) to investigate how market-specific or
product-specific characteristics may alter the incentives in markets with dual reputations.
2
A significant stream of literature, referenced in Menapace and Moschini (2010), considers the case in
which GIs set minimum quality standards. Provided that consumers are aware of the minimum standards,
then GIs help producers in credibly signaling quality to inexperienced consumers. In the current article, we
consider the more general case in which consumers infer that the quality of two producers within the same
region is correlated. Rather than acquiring information ex ante and then deciding on whether to buy , we
model a world in which consumers learn ex post from their multiple experiences. In our opinion, this
process fits better the case of agricultural products which are repeatedly purchased at a relatively low cost.
3
We assume that wine is an experience good for the purposes of this analysis. However, one could make
the argument that wine is a combination of an experience good and a credence good (perhaps stemming
from advertising). If that is the case, then the analysis is more complicated and not all of our theoretical
results will hold. A theoretical analysis is of collective and firm reputations of a combination of experience
and credence goods is beyond the scope of the current article.
4
Given the presence of both types of reputation, our model (conceptually) nests the private
name only model of Shapiro (1982) and the collective-only model of Winfree and
McCluskey (2005) as special cases. The former was the first to use a dynamic
optimization framework to model markets with private names and showed that reducing
consumers’ ability to assess product quality weakens the incentives to invest in it. The
latter showed how collective reputations are essentially public good resources, and as
such are subject to the tragedy of the commons.
Our study contributes to the literature on several fronts. First, a general
theoretical representation of the firm’s decision process under the assumed dual structure
of reputation is developed. We then consider the case of a regional planner maximizing
the profits of the whole production district (a setting where all firms in a region
collaborate, or a single decision maker owns the complete taxonomy of private and
collective names4), providing insight for analyzing producer and industry welfare.
Second, we study how information lags (i.e. the “speed of consumer learning”
from Shapiro, 1982) and price-range market segments (determining the “cost of being
wrong” in Landon and Smith, 1998) interact in determining equilibrium reputations and
industry welfare. We show that, under specific parameterizations, steady-state private
reputations above and below the collective reputation can occur even when firms share
the same production technology and face the same price incentives. Finally, we consider
the case in which the investment in quality of one agent, referred to as a reputation leader,
affects collective reputation more than the other firms in the region. The rationale is that,
given a positive cost of learning and forming quality expectations, some consumers may
consider the quality of the goods produced by a specific firm as a good indicator or
predictor of the quality of the whole district. This, we find, has a non-trivial effect on
quality investments and overall efficiency of the district.
Theoretical Model and Solution Mechanism
The theoretical framework developed here is a dynamic game to account for strategic
behavior between producers. We seek to model the case in which: I) N risk-neutral
producers in a production district (with no entry) maximize their own net present value of
4
This would be the case for multi-brand or multi-product firms such as Nestle or Kraft.
5
profits over an infinite time horizon, subject to the evolution of beliefs about regional and
firm reputations; II) all firms produce a fixed, constant quantity, but each firm i chooses
its quality level, which is costly5; and III) firm and collective reputation in each time
period are determined via (deterministic) Markov processes, which are partially
controlled by the producers. The assumption in II) is consistent with the model in
Winfree and McCluskey (2005), in which an exogenous price curve p(R) is related to
(collective) reputation R, but firms do not compete for market share in the quantity
dimension.
It is assumed that, when firms compete, each producer makes a quality investment
decision taking the response functions of the others as given (à la Cournot). Assuming a
discount factor equal to δ for each firm, we model the maximization problem solved by
firm i as:
∞
V (ri , r-i , R) = max ∑ δ t ⎡⎣ pi (ri ,t , Rt ) − ci (qi ,t ) ⎤⎦
qi ≥ 0
s.t.
(1)
t =0
ri ,t +1 = ri ,t + γβi ( qi ,t − ri ,t )
rj ,t +1 = rj ,t + γβ j ( q*j ,t (ri , r− i , R) − rj ,t ) ∀j ≠ i
⎛
⎞
Rt +1 = Rt + γ ⎜ wi qi ,t + ∑ w j q*j ,t (ri , r− i , R) − Rt ⎟ ,
j ≠i
⎝
⎠
where ri is the private reputation state variable for firm i, r−i represents the (vector of)
private reputations of all the other firms in the district, and R is the region’s collective
reputation. Indicating a (discrete) time period with t, the cost of producing at quality
level qi,t is captured by the function ci (qi ,t ) , while the market price of the product
depends on reputations according to pi ( ri ,t , Rt ) .
The state-transition equation ri ,t +1 = ri ,t + γβ i ( qi ,t − ri ,t ) portrays how, on the
consumer side, private firm reputations are updated (on average) based on the
discrepancy between reputations and current quality output. The parameter γ simulates
the information lag between the time of production and the time when the quality level is
5
The presence of collective reputation implies that firms in the production region may share a comparative
advantage relative to firms outside of the production region. Such comparative advantage could be
exogenous. Since our focus is limited to a single production region, the quality choice is fully endogenous.
6
revealed. This can be thought of as the market or product-specific ‘speed of consumer
learning’ of Shapiro (1982). βi ∈ (0,1) captures firm-specific brand visibility. Crossfirm differences in β i may be determined by multiple factors such as media coverage,
expert reviews or firm size.6
The transition equations rj ,t +1 = rj ,t + γβ j ( q*j ,t ( ri , r− i , R ) − rj ,t ) ∀j ≠ i represent the
paths of the private reputations of other firms in the industry and are defined as functions
of the state-contingent control q*j ,t ( ri , r−i , R ) for firm j such that this control maximizes the
net present value of firm j’s profits given that the other agents pursue theirs. Overall, the
structure of the model is one where each firm can observe private (and collective)
reputations, and anticipates that each firm will play a Nash strategy subject to the
evolution of the complete system.
The state-transition equation for collective reputation,
⎛
⎞
Rt +1 = Rt + γ ⎜ wi qi ,t + ∑ w j q *j ,t ( ri , r− i , R ) − Rt ⎟ , follows the specification in Winfree and
j ≠i
⎝
⎠
McCluskey (2005).7 This equation provides the mechanism whereby consumers’
expectations regarding aggregate (average) regional quality enter the model as a weighted
average of the firm-specific reputations, with full endogeneity implying wi ≥ 0 and
∑w
i
= 1. While previous work has set the influence of firm quality on collective
i
reputation to the reciprocal of the number of firms in the region, there is no reason to
necessarily believe, a priori, that wi = 1/ N . The existence of one or more “reputation
leaders,” for which wi > 1/ N , corresponds to a situation in which a sizable number of
consumers consider the performance of a particular firm as good indicator of the quality
of the whole region. This could be due, for example, to a larger market share of the
reputation leader, its early entrance in the market, or expected trickle-down effects of
6
In this article, we take these parameters as exogenous.
7
Strictly speaking, Winfree and McCluskey (2005) assumed uniform weighting (i.e., wk =
firms’ investment decision.
7
1
) of each
N
technological/managerial leadership to the other firms in the region (all of which are
exogenous in the model).
The simplifying assumptions of exogeneity of the speed of consumer learning
( γ ), firm visibility ( β i ), and reputation leadership ( wi ) parameters is consistent with the
stream of literature we are extending (notably Shapiro, 1982; and Winfree and
McCluskey, 2005) concepts. Costanigro et al. (2010) argued that the relative weights of
these parameters are mostly driven by product and market characteristics, rather than
producers’ choices. In reality, these assumptions may not hold in the long run: firms may
be able to increase their visibility or take actions to affect their influence in the collective
reputation, perhaps by investing in advertisement, expanding market share, or by other
means. Explicitly modeling these processes would introduce additional factors over
which firms optimize without substantially adding insight into the roles of frequency of
purchase, advertisement level, and market share on investment quality decisions in a noncooperative framework.8
Thus, consistent with prior literature, we choose to proxy the evolution of
consumers’ beliefs and behavior via the state-transition equations (which describe how
consumers update their quality expectations) and the price function pi (ri ,t , Rt ) , which
captures equilibrium price changes as aggregate willingness to pay for a specific
reputation level change. Indeed, with many firms and consumers and if all the relevant
characteristics/attributes are imbedded in the measures of expected quality indexed by ri
and R, then pi (ri ,t , Rt ) can be thought as a hedonic price relationship, and the shape of the
price function is exogenous9. In other words, the price function provides a reduced-form
shortcut to capture from real data how consumers learn and value quality when both
private and collective reputations are at play10. Additionally, it should be noted that this
relationship captures a degree of heterogeneity across the consuming population in terms
8
It should be noted that path dependencies in the evolution of the wine market may have resulted in
positive correlations between visibility and market share and reputation leadership (though, in fact, they are
distinct concepts), which could be modeled by choosing appropriate values for the exogenous parameters
representing these dimensions. We thank an anonymous reviewer for pointing out this likelihood.
9
The case of market power is not considered here, and thus the model best describes markets in which
there are many firms and production districts (e.g. wine). This is consistent with the models of private
reputations presented by Shapiro (1983) and collective reputation presented by Winfree and McCluskey
(2005).
10
We thank an anonymous reviewer for this intuition.
8
of the information they posses about a given product and various differences in tastes and
preferences over product attributes.
The Markov-perfect equilibrium for this discrete-time, N-agent game is thus
characterized by a set of N simultaneous Bellman equations of the form
{
(
Vi ( ri , r− i , R ) = max pi ( ri , R ) − ci ( qi ) + δ Vi r1 + γβ1 ⎡⎣ q1* ( r1 ,… , rN , R ) − r1 ⎤⎦ ,
qi ≥0
r2 + γβ 2 ⎡⎣ q2* ( r1 ,… , rN , R ) − r2 ⎤⎦ ,… , ri + γβ i [ qi − ri ] ,… ,
(2)
⎡
⎤ ⎞ ⎫⎪
rN + γβ N ( q*N ( r1 ,… , rN , R ) − rN ), R + γ ⎢ wi qi + ∑ w j q*j ( r1 ,… , rN , R ) − R ⎥ ⎟ ⎬ .
⎟
j ≠i
⎣
⎦ ⎠ ⎭⎪
The unknowns in the system are the (closed-loop) policy functions qi* ( ri , r-i , R ) and the
firm-specific value functions Vi (ri , r−i , R) . Given the dimensionality of the problem and
the complexity of the mathematical solution, numerical analysis is used to solve the game
and characterize the key results. Following Miranda and Fackler (2002), the solution is
approximated using a 9-node Chebychev polynomial approximation to the unknown
value function. The approximation is then used to represent the policy functions and
simulate results11. However, interested readers may refer to Appendix A for relevant
first-order analytical conditions of the joint reputation game and the industry planning
problem.
To reduce the dimensionality of the game in the simulation exercises, the number
of firms is restricted to two.12 Regardless of the “duopoly in reputation” setup, it is still
assumed that firms have no market power, and the only way a firm can influence product
prices is by affecting its reputation via quality output. In other words, we model an
incentive structure consistent with that of a market with many firms and dual reputation
structure, but choose a duopoly setup for tractability. It is understood that, because of the
public good nature of collective reputations, reducing the number of firms in the district
increases equilibrium qualities and reputations, moving them closer to the industry-wide
optimal quality investment of the regional planner (Winfree and McCluskey, 2005).
Accordingly, our interpretation of the results is qualitative in nature.
11
The software of choice for our simulation was the CompEcon toolbox in MATLAB.
This eases the complexity of programming, diminishes simulation running time and simplifies the
graphical representation and interpretation of our results.
12
9
Function Parameterization
Numerical dynamic programming techniques require specific functional forms for
implementation. Instead of assuming a functional form and a set of parameters, we
utilize a California wine data set to estimate a flexible hedonic model capturing how, in
equilibrium, quality output and reputations relate to product prices 13. Reputations play a
pivotal role in wine markets, and as such, the wine industry offers a valid framework
within which reputation dynamics can be studied, while obtaining some reasonably
general results.
The dataset consists of 9,261 observations obtained from the Wine Spectator
(issues from 1992 to 2003) spanning ten vintages (1991-2000) of blind tasting quality14,
scores (SCORE) for California red wines (see Table 1). Each observation includes the
producing winery, the American Viticultural Area (51 AVA in total), the vintage, and the
price (CPI adjusted to the 2003 base year). The chosen specification is a quadratic form
with an interaction term:
(3)
Pˆlikt = α + β1rit + β 2 rit2 + β 3 Rkt + β 4 Rkt2 + β 5 Rkt rit ,
where Plikt is the price of the lth wine produced by winery i from region k in year t and r
and R are proxies for private and collective reputations, respectively. Mimicking the
state-transition equations in the theoretical model, we compute these reputation proxies as
moving average processes of previous quality rating scores15.
Following Costanigro, McCluskey and Goemans (2010), the hedonic model in (3)
is estimated via quantile regression (Koenker and Basset, 1978) at different conditional
13
This model is a modification of the model by Costanigro, McCluskey, and Goemans (2010).
A justification for the use of wine ratings as proxies for quality is that they are blind quality assessments
by experts, exogenous to prices.
15
More formally, and using the subscript i for the wine, j for the winery and k for the regions, the kth AVA
14
reputation is defined as Rkt =
1⎡
Rk ( t −1) + avg ( SCOREijk ( t −1) ) ⎤⎥ , where t is the issue year of the Wine
⎢
2⎣
k
⎦
Spectator magazine, and avg the average operator applied to all wines produced in the kth AVA, rated in
k
period t-1. The analogous private reputation construct relative to the jth firm is
1⎡
⎤
rjt = ⎢rj (t −1) + avg ( SCOREijk (t −1) ) ⎥ . The first observation of each series is missing, and the second is
2⎣
j
⎦
calculated using the average quality score of the first year in which a winery/AVA appears in the dataset,
producing 6,115 complete observations.
10
quantiles (the 15th, 50th, and 75th), in order to capture the changing structure of the
reputation dynamics across wines in different price segments. While the wide range of
prices observed in the wine market is somewhat unique, simulation results based on the
different pricing functions can be (roughly) interpreted as illustrating the incentive
structure in markets for cheap, medium and expensive products. Consistent with
Costanigro, McCluskey, and Goemans (2010), we expect private reputation to become
more valuable (relative to collective), as one transitions from cheaper to more expensive
products. The intuition is that the increased cognitive and search effort necessary to form
quality expectations for the large number of firm names is justified only when the price
of the good is large enough.
In quantile regression, parameters estimates are obtained by solving the
minimization problem: minp ∑ ρτ ( yi − xi 'β ) , where ρτ represents a function which, by
N
β ∈ℜ
i =1
asymmetrically weighting residuals, yields the τ th conditional quantile ∈ [ 0,1] , y is the
regressand, x are the regressors, and p specifies the number of parameters to be
estimated. Since the weighting function differs across quantiles, our estimations produce
three sets of benchmark parameters, which may be interpreted as distinct subsets of the
market with differing a) magnitudes of the marginal effects of reputation changes (both
private and collective); b) relationships between the marginal relative effects of private
vs. collective reputations.16 Regression results are reported in Table 2.
Given that the minimum/maximum private and collective reputation measures
observed in the sample are ri ∈ [ 62.00, 96.63] ∀i and R ∈ [ 74.66, 91.00 ] , our results
suggest that the predominant relationships are pr ( ri , R) > 0 , pR (ri , R) > 0, prr ( ri , R) > 0,
pRR ( ri , R) ≥ 0, and prR (ri , R) > 0 , for all quantiles. With the exception of the privatecollective cross effects, which are perhaps ambiguous on a priori grounds17, all signs
meet theoretical expectations (see Rosen, 1981, on the “economics of superstars” for an
16
In the simulations that follow, it is assumed that all firms in a production district face the price function
for that quantile for all time periods in the simulation; that is, for each quantile q, piq ( ri ,t , Rt ) = p q ( ri ,t , Rt )∀i, t, or
equivalently, firms take their price function as given at the beginning of the planning horizon, and do not or
cannot migrate across quantiles.
17
The only novel empirical result relates to the finding that, for California wineries, private and collective
reputations are complements.
11
argument supporting the increasing marginal benefit of reputation), with the proviso that
the complementary relationship between collective and private perceptions of quality
might be a wine-industry specific result. Examined across quantiles, empirical results
show that the marginal impact of an increase in reputation is generally greater for wines
in the high-price market segment.
In contrast to the price data, information on the cost side of the market is
unavailable. Therefore, we calibrate a cost function that ensures a unique steady-state
equilibrium falling within the range of the observed data for the median quantile results
reported in Table 2. For all firms in the production district, we assume a linear marginal
cost function of the form ci′( qi ) = c′( qi ) = α1 + α2 qi , such that the marginal cost of quality
investment is increasing in quality.18 While we make no claims as to the
representativeness of this function for the industry as a whole, it allows for a numerical
solution to the problem, as well as offering a first-order approximation to the underlying
form of the cost functions. Again, the reader is nevertheless cautioned that more
attention should be paid to qualitative model results, rather than the specific quantitative
figures.
Based on these assumptions, the functional forms relevant for the simulation of
our two-player game, are: c′( qi ) = −323.571 + 3.7857 qi for all quantiles,
and pr ( ri , R ) = −56.62 + 0.36ri + 0.32 R and pR ( ri , R ) = −56.66 + 0.38R + 0.32ri , i=1,2, for
,
the median quantile. Marginal price functions for the 15th and 75th conditional quantiles
can be derived from Table 2, and it is assumed that all firms discount the future with a
factor of δ = 0.95 .19
Results
Policy Response Function and General Incentives (Median Quantile)
To illustrate the fundamental incentives of each firm in the dual reputation scenario, we
first consider the case of fully homogeneous firms (that is β1 = β2 and w1 = w2 ). Figure 1
presents the policy (best response) function of Firm 1, assuming uniform speed of
18
The adoption of identical marginal cost functions seems reasonable for firms operating in the same
production district.
19
This implies an approximate interest rate of 5.3%
12
adjustment parameters (γ = 0.2, β1 = β 2 = 1), and no reputation leader (w1 = w2 = 0.5) .
Note that the overall speed of adjustment parameter is less than one, indicating a lag
between investment in quality and consumers’ updating of reputations. In the upper
panel, we present a three-dimensional cross section in which Firm 1’s optimal quality
investment is mapped against the private reputation of Firms 1 and Firm 2 while
collective reputation is held constant at the node closest to the steady-state value.20 In the
lower panel, Firm 1’s reputation and collective reputation vary, while Firm 2’s reputation
is held constant.
In each case, we see that optimal investment in quality is increasing in own
private reputation, the other firm’s reputation, and the collective reputation, though the
magnitudes differ. Thus, a decision by another agent to invest in quality induces similar
behavior by the other agents, primarily through the price effect of collective reputation.
This result is analogous to what Carriquiry and Babcock (2007) show for the case of a
duopoly with collective reputations. Even though the slope of the value function implies
that r− i and R have positive marginal values,21 the response is not fully symmetric: a unit
increase in the reputation of Firm 2 (or the collective reputation) will not be matched by a
corresponding increase in investment by Firm 1. To simplify, under a dual reputation
structure returns from private reputations mitigate the free-riding behavior associated
with common-property resources.
Figure 2 illustrates the paths to the steady states and the role played by the pricing
equations, again for the case of homogenous firms. Initial private reputations are set at
low level for Firm 1 and high for Firm 2 ( r1 < R < r2 ) . Regardless of the initial
conditions, firm homogeneity implies that private reputations, collective reputations, and
quality investment all converge to a common steady state. Also note that when the
system is in equilibrium, reputations and quality choices coincide
(r
τ
1
= q1τ = r2τ = q2τ = Rτ ) . The speed of adjustment parameters ( γ and βi ) determine the
amount of time required to reach the steady-state, with higher parameter values inducing
20
At solution nodes, the solution to the value functions embodied in the Bellman equations are exact; off of
these nodes, mean errors are of the magnitude 2(10-9).
21
Given the price function, this marginal value (co-state) is not only positive, but increasing in r− i and R,
though this result is more pronounced once heterogeneity is introduced.
13
a rapid approach. The main result here is that the equilibrium quality and reputations
increase from the low to the high conditional quantiles (figure 2). While this result is
consistent with theoretical expectations (see figure III in Shapiro, 1983), in our
simulations it is driven by the empirical estimation of the pricing function, rather than by
a priori choices of parameters. An interpretation is that, since consumers are willing to
pay more for good reputations when facing high product prices (the cost of “being wrong
is higher”), in the higher price segments producers capitalize greater returns from
investing in quality. This, in turn, increases the equilibrium quality and reputations.
Equilibrium Quality, Efficiency and Polar Cases
Based on theoretical expectations, two principal factors will influence investments in
quality when private and collective reputations coexist: the degree to which consumers
are able to immediately assess quality (as in Shapiro, 1982), and the “public good”
dynamics arising from the presence of a collective name (as in Winfree and McCluskey
2005), which imply an inefficient investment in quality. By specifying alternative
parameterization of the simulation one can investigate how specific market conditions or
product characteristics may diminish or foster industry incentives to invest in quality.
Before considering some specific cases, however, we consider two polar scenarios
to be used as benchmarks. In the first one, the dual reputation competitive scenario
represented by equation (1) is modified to model the decisions of a regional planner
maximizing industry-wide profits. The intent here is determining how much more quality
investment (with respect to the competitive outcomes) would be imposed by the planner,
and thus illustrate the case in which producers fully cooperate (and such cooperation is
sustained). In the second case, firm visibility parameters are set to zero and firms are left
to maximize their own profits, thereby modeling the case of an industry with only
collective reputations22.
22
More in detail, the regional planner’s solution is obtained by maximizing the sum of profits across firms,
subject to the equations of motion (see Appendix A) and exogenous pricing structure. The
parameterization of the collective-only model is slightly more problematic: while setting β1 = β 2 = 0
serves the purpose of dampening to zero the marginal benefits from private reputation, for the sake of
comparison we must set the private reputation constant at some level in the pricing equation (it would be
2
misleading to simply truncate the pricing function to Pˆikt = α + β 3 Rkt + β 4 Rkitt ) and the point chosen will
14
The regional planner will invest in quality so that the marginal cost of investment
for each firm equals the discounted marginal benefits for the industry, thereby including
the total contribution to both private and collective reputations. In the dual reputation
strategic game, each firm also considers the marginal value of own and collective
reputation, but positive externalities accruing to other firms are not internalized. In the
collective-only model, these marginal benefits are smaller still, as the inability to
(
)
influence private reputations Vi ,ri ( ⋅) γβ i = 0 induces an even further underinvestment.
Figure 3 illustrates the results by juxtaposing, for various parameterizations, the
equilibrium reputations under the regional planner (dual reputation cooperative), the
corresponding strategic game (dual reputation noncooperative), and the collective-only
game (collective noncooperative).23 As expected, the level of investment in quality is
increasing in the aggregate “speed of adjustment” term, γβ i : the longer the time lag
between quality investment and the realization of the associated response in revenues, the
more firms will discount the value of reputations and produce at lower quality.
The ratios between the two non-cooperative outcomes and the regional planner
solutions (in percentage terms in figure 3) provide a measure of industry losses due to
lack of cooperation. Interestingly, even though the magnitude of the investment in
quality is increasing in the speed of adjustment, inefficiency losses are largest when
consumers discover quality instantaneously ( γ = β1 = β 2 = 1 ), and each firm immediately
sets quality investment to the long-run steady-state level. 24 Conversely, the inefficiency
is smaller when quality is difficult to observe. The interpretation is that, when
reputations are hard to build because of exogenous factors, returns from investing in
quality are not capitalized in either pricing function, and there is simply not much to lose
from lack of cooperation. From a policy standpoint, this suggests that regulators wishing
influence results. In order to keep the results as conservative as possible, private reputations for each firm
are set at the “optimal” steady state levels obtained in the regional planner scenario.
23
Note that because the firms are homogenous in this simulation, in the long-run private and collective
reputations converge.
24
The fact that equilibrium outcomes are quite close to 100% is a direct consequence of reducing to two the
number of firms in the district. The magnitude of the inefficiency will be much more significant when
more than two firms are present, but the relative efficiency rankings across the different scenarios will
remain unchanged.
15
to increase product quality should first increase transparency and consumers’ ability to
recognize quality, and only after target free-riding behavior on the producers’ side.
Reputation Leaders and Quality Laggards
We now relax the assumption of firm homogeneity to study the reputation dynamics
induced by differential availability of information regarding quality performance and
consumer perceptions. Two cases are considered: one in which consumers can more
easily update their expectations on the quality output of certain firms (which is depicted
by allowing for variation across β i ) and one in which consumers use the quality of a
specific firm as an indicator or predictor of the quality of the entire district (variations in
wi ) .
Differing Firm Visibilities
Sources of information that are used to form quality expectations include the consumer’s
experience, expert reviews, and advertisement. In many cases, these elements might vary
across firms. Alternatively, consumers may be exposed more to the products of certain
firms (e.g. when market share is not equally divided among firms or there is a dominant
firm). Figure 4 presents the case in which Firm 1 is less visible than Firm 2 ( β1 < β 2 ).
The primary result here is that differences in these (exogenous) firm-specific parameters
induce non-convergent steady state reputations, specifically r1τ < Rτ < r2τ .25 This shows
that heterogeneity in output quality within a region is not necessarily due to unequal
access to production technology, but rather may be the result of demand-side conditions
related to consumers’ differential updating and learning. Also visible in figure 4 is that,
as the chosen pricing segment increases, the steady state collective reputation also
increases, and so does the deviation of each agent’s private reputation from the collective
level. As the figure shows, in the higher quantile the less-visible firm invests well below
the collective reputation level. That is, underinvestment becomes more blatant in the
highest pricing segment, where the returns from reputations are greatest.
25
Obviously, a similar (but trivial) result can be obtained assuming heterogeneity in marginal costs.
16
Reputation Leaders
We defined a reputation leader as one for whom quality performance has a prominent
weight ( wi > 1/ N ) in determining consumers’ expectations about the quality of a region.
This section investigates the incentive structure and efficiency outcomes induced by the
presence of a reputation leader, maintaining the assumption that Firm 1 and Firm 2 are
the only source of information used in developing the collective reputation ( w1 + w2 = 1).
Figure 5 shows the equilibrium firm and collective reputations of the dual
reputation strategic game (several parameterizations); and compares them to the regional
planner (cooperative) solution. From left to right, the reputation leadership of Firm 1
increases, while firm homogeneity is imposed in all other aspects. Results highlight how
the regional planner will asymmetrically increase the investment of the reputation leader,
and decrease the laggard’s. In the competitive versions of these games we see a similar
behavior, yet the investment of the leader becomes increasingly sub-optimal as his/her
weight on the collective reputation grows larger; while the opposite is true for the
laggard. In summary, the presence of a reputation leader increases the collective
reputation, but also the overall level of inefficiency26 and the associated industry losses.
In the parameterization with instantaneous updating and the highest level of
reputation leadership (w1=0.95) the investment of Firm 2 is almost irrelevant, and the
collective reputation responds to the actions of the leader much like if it were its own
firm reputation. Thus, it is somewhat counterintuitive that the presence of a reputation
leader increases the inefficiency of the overall market due to public good dynamics. 27
The economic explanation is that, while reputation leadership influences the evolution of
the collective reputation via the relative weights in the state equation, a similarly
proportional distribution of the resulting benefits does not occur, and every firm in the
district receives an equal share28. A regional planner imposes a very asymmetric quality
investment policy to account for the sizable spillovers resulting from the leader’s
26
Just as before, slower speeds of adjustment and visibility decrease quality but increase efficiency (not
shown in figure). The primary result is qualitatively unaffected
27
Firm 1 faces a per-unit loss of $6.46 (earning $29.00 per bottle compared to $22.54) and Firm 2 loses
$3.65 (earning $24.65 versus $21.00).
28
This, we argue, is quite realistic, and applies to the cases of firm and regional reputation, firms and
variey, or more generally firms and commodity produced (as in the brand vs. generic advertisement
literature).
17
investment. On the other hand, in a competitive setting the reputation leader sees things
quite differently: the high weight on collective reputation implies a large cost share of
maintaining good (optimal) collective reputation, yet the firm is unable to collect all the
benefits, which accrue to the district as a whole. The externality arising from the public
good dimension of the problem is therefore exacerbated, and the leader under-invests by
a relatively large margin, driving the collective reputation efficiency down. However,
since it is optimal for the laggard to invest relatively less in the cooperative solution, the
relative efficiency of this firm is actually highest across the three scenarios. Finally,
Figure 6 shows that, consistent with previous reasoning, the inefficiency induced by a
reputation leader is minimal in the cheaper pricing segments, and largest in the high price
ones.
Discussion and Conclusions
In this article, we used differential game theory to study how and why profit-maximizing
firms invest in quality when price premia for good reputations are associated with both
private and collective names, and these reputations evolve in accordance with individual
firm behavior. Previous research has typically focused on either private or collective
reputations independently, therefore disregarding the interactions intrinsic to dual
reputation markets.
To ground results to markets for experience goods, wine data was used to
empirically estimate the functional relationships between product prices and reputations.
Equilibrium outcomes from a variety of parameterizations (each representing alternative
market conditions) were compared and contrasted with the industry-wide optimal
investment in quality. Results were then used to qualitatively gauge the efficiency (in
terms of relative quality) of non-cooperative outcomes, and thus the potential industry
gains from cooperation.
Consistent with theoretical predictions and previous literature, our results showed
that equilibrium quality and reputations increase as it becomes easier for consumers to
learn about quality and form their expectations. Similarly, results show that without
coordinated action industry-wide investment in quality will be inefficient - the classic
public good result arising from the diffused ownership of the collective name.
18
Interestingly, inefficiencies owed to public good dynamics are found to be larger in
transparent markets, where reputations are quickly formed and updated, and there are
thus larger potential gains from investing in quality.
The use of multiple pricing functions, specific to market price segments, yielded
another set of results. First, the optimal quality investment is found to increase across
conditional price quantiles. That is, regardless of comparative advantage (i.e. cost
functions), identical firms will choose to produce at higher quality when entering the
high-price segment. However, the relative efficiency of the non-cooperative outcomes
decreases in the price quantiles. Our interpretation of these results somewhat reverses
the causality between product quality and prices. Consumers are willing to pay more for
good reputations when buying expensive items, because the cost of experiencing poor
quality is higher. This creates an incentive for producers to invest more, fulfilling the
prophecy that high prices signal high quality. However, it is precisely in these markets,
where the potential gains from good reputations are sizeable, that the tragedy of the
commons is most pronounced, with greater damage to the producers who are unable to
cooperate.
Another set of results highlights how dual reputation structures, with their
combination of private and public incentives, are inherently prone to intra-regional
controversies. First, we find that diverging steady states in private reputations, above and
below the collective reputation level, can be due to differences in firm visibility, rather
than comparative advantage for quality. Thus, a less visible firm may be accused of freeriding on the efforts of the others (which is technically untrue: every firm in our model
behaves in the same way given its exogenous visibility). Second, we find that the
equilibrium collective reputations increase in the presence of a reputation leader. In this
case, the discrepancy between the optimal (cooperative) investment and the competitive
solution increases with the magnitude of reputation leadership, and it is the leader who
could be accused of not doing enough to sustain the good name of the region.
It is curious that, against the common “little guys versus the big guy” mantra, it
may make economic sense for the laggard(s) to subsidize the quality investment of the
reputation leader, and share more of the collective reputation costs. Admittedly, this
result is conditional on the exogeneity of the firm visibility and leadership weight
19
parameters in the reputation-transition equations, which is a maintained assumption in
this article. In reality, this may not be the case: at least in the long run, the laggards
might be able to modify their firm visibility (the β i ) or take actions to affect their
influence in the collective reputation (the wi ), perhaps by investing in advertisement,
expanding market share, or by other means. However, it is not clear that it would be in
the best interest of the laggard to do so, since the returns from collective reputation are
much higher in the presence of a reputation leader; and, given a choice, firms would
much rather invest in their own firm visibility than in assuming the thankless role of the
regional reputation leader. Thus, a promising (if complicated) avenue to expand this
work is to first understand how reputation leadership and own firm visibility are related
(here they are independent), and then embed that information in a model with
endogenous weights and visibilities.
20
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21
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22
Table 1. Descriptive Statistics of Dependent and Independent Variables
PRICE*
SCORE
r
R
**
N
9261
9261
7717
9074
Mean
$37.18
86.54
86.65
86.25
Min
$6.05
60
62.00
74.67
p25
$19.76
84
85.00
85.42
p50
$27.12
87
87.00
86.24
p75
$39.78
89
88.48
87.68
Max
$2,140
99
96.63
91.00
*
CPI adjusted to 2003
**
Differences in number of observation across variables are to be attributed to non-AVA wines,
scarcely populated series of quality ratings or missing data.
23
Table 2: Pricing Equations for the Low, Median and High Price Segments (Quantile
Regression Results)
Quantile
Quantile
Quantile
15
50
75
-20.96***
-56.62***
-108.38***
r
(3.17)
(3.55)
(12.65)
2
0.04**
0.18***
0.47***
r
(0.01)
(0.02)
(0.06)
-23.02***
-56.66***
-98.38***
R
(5.43)
(5.17)
(13.07)
2
0.05
0.19***
0.41***
R
(0.04)
(0.03)
(0.08)
0.18***
0.32***
0.37***
R*r
(0.04)
(0.03)
(0.07)
1766.38*** 4659.23*** 8548.18***
Constant
(248.50)
(281.51)
(699.18)
N=6115
19.76
27.12
39.78
Price
Mean r
85.00
87.00
88.48
Mean R
85.42
86.24
87.68
a
Marg r
$1.12
$2.81
$7.17
Marg Ra
$1.78
$3.54
$6.80
Standard errors in parentheses.
** Significant at 5%, *** Significant at 1%
a
Marginal effects evaluated at means.
24
Figure 1: Policy Response Functions of Firm 1. Homogenous Firms,
w1 = w2 = 0.5, γ = 0.2, β1 = β 2 = 1
Optimal Quality Investment
Optimal Policy Rule, Player 1, Reputation Game, Public Rep = 86.3077
86.8
86.6
86.4
86.2
95
95
90
90
85
85
Private Rep Player 2
Private Rep Player 1
Optimal Quality Investment
Optimal Policy Rule, Player 1, Reputation Game, Player 2 Rep = 86.3077
87
86.5
86
95
95
90
90
85
85
Public Rep
Private Rep Player 1
25
Figure 2: Paths to Steady State for Three Conditional Quantile Price Functions. Homogenous Firms, w1 = w2 = 0.5, γ = 0.2,
β1 = β 2 = 1
Quantile 15
Quantile 50
r2
Quantile 75
r2
r2
R
R
R
r1
r1
r1
26
Figure 3: equilibrium reputations/quality for games with dual (cooperative,
noncooperative) and collective only (noncooperativea) reputation structures. Ratios
between cooperative and non-cooperative outcomes are in percentages. Speed of
adjustment decreases from the left ( γ * βi = 1) to the right quadrant ( γ * βi = 0.01) .
Homogeneous firmsb ( β1 = β2 ) , median quantile pricing equation.
87.5
87
99.21%
86.5
99.44%
99.43%
86
98.40%
99.02%
99.55%
99.50%
98.79%
85.5
85
γ=βi=1
Dual Rep. Cooperative
γ=1, βi=.05
γ=.2, βi=1
Dual Rep. Noncooperative γ=.2, βi=.05
Collective NonCooperative
a: private reputations are set constant at the dual cooperative equilibrium
b: homogenous firms imply that r1 = R = r2 (see figure 2)
27
Figure 4: Paths to Steady State for Three Conditional Quantile Price Functions. Heterogeneous Firms with Different Visibility
Parameters, w1 = w2 = 0.5, γ = 0.2, β1 = 0.05, β 2 = 1
Quantile 15
Quantile 50
Quantile 75
r2
r2
r2
R
R
R
r1
r1
r1
28
Figure 5: equilibrium reputations/quality for cooperative outcomes (Firm1, collective,
Firm2), non-cooperative outcomes (Firm1, collective, Firm2) and ratios between
cooperative and non-cooperative outcomes (in percentages). Reputation leadership
increases from the left ( w1 = 0.5 ) to the right quadrant ( w1 = 0.95 ). Dual reputation
structure, median quantile pricing equation and instantaneous speed of adjustment
( γ * βi = 1 )
89
88.5
88
98.29%
98.37%
87.5
98.80%
98.98%
87
99.21%
99.52%
86.5
99.77
86
85.5
85
84.5
w1=.50, w2=.50
w1=.75, w2=.25
w1=.95, w2=.05
Firm 1 Cooperative
Collective Cooperative
Firm 2 Cooperative
Firm 1 Noncooperative
Collective Noncooperative
Firm 2 Noncooperative
29
Figure 6: equilibrium reputations/quality for cooperative outcomes (Firm1, collective,
Firm2), noncooperative outcomes (Firm1, collective, Firm2) and ratios between
cooperative and non-cooperative outcomes (in percentages) in the presence of a
reputation leader ( w1 = 0.95 ). Conditional quantile pricing function increases from the
left (0.15) to the right quadrant (0.75), dual reputation structure and instantaneous speed
of adjustment ( γ * βi = 1 )
96
94
92
93.79 94.02
90
88
98.81
98.30 98.37
99.33 99.36
86
99.77
99.93
84
Quantile 15
Quantile 50
Quantile 75
Firm 1 Cooperative
Collective Cooperative
Firm 2 Cooperative
Firm 1 Noncooperative
Collective Noncooperative
Firm 2 Noncooperative
30
Appendix A: First-order conditions of the problems
Joint, Noncooperative Game with both Private and Collective Reputations
The first-order conditions for each player i in the non-cooperative game are derived from
the Kuhn-Tucker and Envelope Theorems applied to the Bellman equation (Miranda and
Fackler, 2002):
−c′( qi ) + δ ⎡⎣Vi ,ri (⋅) γβ i + Vi ,R (⋅) γ wi ⎤⎦ = 0
Vi ,ri (⋅) = pri ( ⋅) + δVi ,ri ( ⋅) (1 − γβ i ) + δ ∑Vi ,rj (⋅) γβ j q j ,ri (⋅) +δ Vi ,R ( ⋅) ∑ γ q j ,ri (⋅) w j
j ≠i
(
j ≠i
)
Vi ,rj (⋅) = δ Vi ,rj (⋅) ⎡1 + γβ j q j ,rj (⋅) − 1 ⎤ + δ ∑ Vi ,rk (⋅) γβ k qk ,rj (⋅)+δ Vi ,R (⋅) ∑ γ q j ,rj (⋅) w j ∀j ≠ i ,
⎣
⎦
k ≠i , j
j ≠i
⎡
⎛
⎞⎤
Vi ,R ( ⋅) = pR ( ⋅) + δ ∑Vi ,rj (⋅) γβ j q j ,R (⋅) +δ Vi ,R ( ⋅) ⎢1 + γ ⎜ ∑ q j ,R (⋅) w j − 1⎟ ⎥
j ≠i
⎢⎣
⎝ j ≠i
⎠ ⎥⎦
plus the equations of motion for each state variable.
In essence, these conditions suggest that is it optimal for each firm to invest such
that the current-period marginal cost of investment is equal to the marginal benefit of
doing so, with this marginal benefit defined as the (discounted) increase in value from
both private and collective reputation, with the discount depending on the discount rate,
the speed of adjustment parameters, and the weight of own reputation on the collective.
Industry Planner Model with both Private and Collective Reputations
In contrast, the first-order conditions for the regionally optimal solution
characterize the solution to the Bellman equation
31
⎧N
J (r, R) = max ⎨∑ ( pi ( ri , R) − ci ( qi ) ) + δ J i r1 + γβ1 ⎡⎣ q1 − r1 ⎤⎦ , r2 + γβ 2 ⎡⎣ q2 − r2 ⎤⎦ ,…
q ≥0
⎩ i =1
(
⎡
⎤ ⎞ ⎫⎪
rN + γβ N ( qN − rN ), R + γ ⎢ ∑ wi qi − R ⎥ ⎟ ⎬ ,
⎣ i
⎦ ⎠ ⎭⎪
and are defined as:
− c′( qi ) + δ ⎡⎣ J ri ( ⋅) γβ i + J R ( ⋅) γ wi ⎤⎦ = 0 ∀i
J ri ( ⋅) = pi ,ri ( ⋅) + δ J ri ( ⋅) (1 − γβ i ) ∀i
J R ( ⋅) = ∑ pi , R ( ⋅) + δ J R ( ⋅) (1 − γβ i ).
i
Note that in contrast to the non-cooperative game problem, the regionally optimal
solution accounts for the full effect of collective reputation through the equation for
J R ( ⋅) , and that investment in firm-specific reputations takes this into account without
any strategic interaction effects.
32