Title
Author(s)
Developing Trusting Relationships Through
Communication
YOKOYAMA, Izumi; OBARA, Takuya
Citation
Issue Date
Type
2015-02
Technical Report
Text Version publisher
URL
http://hdl.handle.net/10086/27045
Right
Hitotsubashi University Repository
Department of Economics, Hitotsubashi University
Discussion Paper Series No. 2015-03
Developing Trusting Relationships
Through Communication
Izumi Yokoyama and Takuya Obara
February 2015
1
Developing Trusting Relationships Through
Communication∗
Izumi Yokoyama†
Faculty of Economics, Hitotsubashi University
Takuya Obara
Department of Economics, Hitotsubashi University‡
February 10, 2015
Abstract
In this paper, we analyze the formation of trusting relationships among people through
communication. To foster trusting relationships, individuals must disclose private and personal
information. However, disclosing such information has both costs and benefits; therefore, both
parties must decide on the optimal level of self-disclosure based on a variety of factors, such
as the current level of intimacy and the benefits of deepening this intimacy. We constructed
an economics model that explains Altman and Taylor (1973)’s social penetration theory with
a focus on one of its most important results: “reciprocal self-disclosure” increases during the
initial stages of intimacy and then declines after a certain level of intimacy has been reached.
JEL Classification: Z13, D03
Keywords: Communication model, Stackelberg game, Self-disclosure
∗ We
wish to thank Hiroyuki Chuma and Isao Ohashi, who provided invaluable advice.
a Ph.D. in Economics from the University of Michigan in 2013. Current Position: Assistant Professor,
Department of Economics, Hitotsubashi University in Japan. Postal Address: 2-1, Naka, Kunitachi, Tokyo, Japan,
186-8601. Email: [email protected]. Tel: +81-42-580-8598. Fax: +81-42-580-8598.
‡ Ph.D. student. 2-1, Naka, Kunitachi, Tokyo 186-8601, Japan. Email: [email protected]
† Received
2
1
Introduction
While communication is a means of facilitating understanding, it is also a means of building a
trusting relationship between two individuals. Humans cannot foster trusting relationships without confessing something of themselves to one another. In other words, to establish a trusting
relationship, self-disclosure by both parties is required.12
However, self-disclosure has both benefits and risks: As stated above, one of its great benefits is the formation of trusting relationships. Another benefit is the one-sided positive effect of
autocatharsis, whereby just talking about personal burdens “lightens the load.” In contrast, selfdisclosure brings the risk that the other party will reveal private and personal information to others,
for which the attendant cost is psychological resistance. The questions arise, then, of what is the
most rational way for humans to form relationships through self-disclosure.
Many psychological studies have been done on self-disclosure. Altman and Taylor (1973)
found that as interpersonal interactions deepen, self-disclosure progresses from the shallow to the
deeper regions of personality. They established this finding as the theory of “social penetration.”34
Furthermore, they noted that although reciprocal self-disclosure occurs up to a certain level of
intimacy, it declines once this level is reached (Altman and Taylor 1973). The existence of such
behavioral trends in self-disclosure suggests that people follow a kind of decision-making process
when they engage in self-disclosure. Thus, in this paper, we explain the behavioral trends observed
1 According
to Jourard (1971), self-disclosure is “the act of making yourself manifest, showing yourself so others
can perceive you.” That is, self-disclosure is the conveyance to another party of private and personal information, such
as feelings, thoughts, values, and desires; experiences and background; and future hopes.
2 The successful formation of a trusting relationship only occurs when an act of self-disclosure is favorably received
by the other party, who then reciprocates with similar self-disclosure (Derlega 1984).
3 Indeed, there are many papers that support social penetration theory (Altman and Haythorn 1965, Ando 1978,
Reiser and Altman 1976, Morton 1978, Taylor and Altman 1975, Taylor et al. 1969). In contrast, there are also papers
that criticize social penetration theory (Berg 1984, Berg and McQuinn 1986, Hays 1984, 1985).
4 Chaikin and Derlega (1974) reported that private disclosure is considered more appropriate with those individuals
considered intimate friends than with new acquaintances. Altman and Taylor (1973) found that only 2% of their
study participants indicated having disclosed private information to new acquaintances. In addition, Won-Doornink
(1979, 1985) examined whether the phenomenon proposed by Altman and Taylor (1973) and Altman (1973) would
hold using data gathered in South Korea. They confirmed a curvilinear association between the stage of interpersonal
relationship and the degree of reciprocity of intimate self-disclosure. The results of Altman (1973), and Altman and
Taylor (1973) were developed primarily on American subjects. Therefore, Won-Doornink (1979, 1985) suggested that
the reciprocity phenomenon may universally hold.
3
in experiments using a tool of economics. We demonstrate that while the sensitive process of forming a trusting relationship between two individuals appears to be unrelated to rational behavior, it
can be explained by the rational human being assumption found in economics.
As a paper that constructs an economics model of communication, this work is closely connected to that of Dewatripont and Tirole (2005).5 Dewatripont and Tirole (2005) examined communication as a means of promoting “understanding”, where, in the course of persuading another
to follow a recommended project, the persuader gets the other party to understand the project’s
pros and cons and/or details. However, along with this “promotion-of-understanding” aspect of
communication, there is also the important aspect of “fostering a trusting relationship”.67 In this
paper, we deal with the latter aspect of communication in the basic model and consider both aspects of communication in an extended model. We consider two human beings; a sender and a
receiver.
In self-disclosure communication, unlike in communication “to promote understanding,” the
order of self-disclosure is clearly given; therefore, the problem is solved as a Stackelberg game,
with the sender as the leader. Both parties decide on the optimal level of self-disclosure based
5 There
is a significant body of theoretical literature related to communication. Some communication models have
been established in non-economics literature to understand communication psychologically or conceptually (Bedford
and Baladouni 1962, Derlega and Grzelak 1979, Kenkyukai 1986, Ohashi and Osada 1987, Nishikawa and Komaki
2002). More recently, some communication models have focused on strategic interactions using economics models
between a sender and receiver. Crawford and Sobel (1982) investigated the characterization of Bayesian Nash equilibria within the context of a sender observing a person who is her “type” and then sending a signal that expresses a noisy
estimate of this type to the receiver. The research showed that preference divergence between two parties causes the
sender to withhold information. Moreover, as preference divergence increases the amount of information disclosed by
the sender decreases. Krishna and Morgan (2004) extended this model to include the scenario wherein a sender and
receiver meet face-to-face before the sender communicates her final recommendation to the receiver. This amendment
considers that if the receiver possesses useful information unknown by the sender, the dialog between the two parties
enables the sender to enhance her final recommendation by obtaining information sent by the receiver. This environment leads to useful information transmission (the sender discloses a greater amount of information) and results
in payoffs for both parties. Furthermore, the research showed the existence of an equilibrium that is Pareto superior
to all of the equilibria identified by Crawford and Sobel (1982). Crawford and Sobel (1982), Krishna and Morgan
(2004), and Dewatripont and Tirole (2005) all assume that the relationship between the sender and the receiver is the
dichotomy, which means that information flows in one direction.
6 Stein (2008) developed a model of bilateral conversation in which players exchange ideas, and information flows
in both directions. Our model is similar because the receiver can decide whether to reciprocate the sender’s selfdisclosure. However, Stein (2008) examined the condition of competing players sustaining a conversation in which
each player truthfully reports to the other. Therefore, the goals of their research were different from those of the
current study.
7 Penley and Hawkins (1985) focused on communication within an organization (particularly, communication between supervisors and subordinates).
4
on factors such as the degree of existing intimacy, costs, and the payoff to be gained from the
formation of a relationship.
The main conclusions of this report are as follows. When the foundational level of intimacy
is below a certain level, the risk to the receiver of his/her personal information being revealed
by the sender is perceived to be high; therefore, the receiver does not reciprocate self-disclosure.
Anticipating this, the sender has no incentive to self-disclose and, thus, without prior communication (hereafter a “cue” communication), self-disclosure does not occur. In a situation like this, the
sender engages in a “cue” communication for a while before self-disclosure, including conversation with shallow content, to get the receiver to perceive the sender as trustworthy. The receiver
also self-discloses only if he/she judges the sender as highly trustworthy based on the “cue” communication.
In contrast, when a certain level of trust exists between the two parties, the receiver reciprocates
the sender’s self-disclosure even if a slight risk surrounds the trustworthiness of the sender, as the
benefits of self-disclosure outweigh the costs. Aware of this, the sender directly self-discloses,
avoiding a “cue” communication, which is costly in terms of time and physical resources.
Furthermore, the higher the level of intimacy between the two parties the more frequently selfdisclosure with deep content occurs. At the same time, there is a change in the quality of the selfdisclosure. That is, with increased intimacy, the focus moves away from the “trusting relationship
fostering” elements of self-disclosure toward self-completion elements, such as “autocatharsis.”
Because the payoff from the act of self-disclosure itself is obtained independent of the other party, it
does not decline as the level of intimacy rises. In contrast, the cost of self-disclosure is a decreasing
function of the level of intimacy. Thus, when an individual decides upon a level of self-disclosure at
which the marginal benefit is the same as the marginal cost, the proportion of the overall marginal
benefit accounted for by self-completion effects rises as the level of intimacy increases. This
indicates that the tacit aim of self-disclosure as the level of intimacy rises shifts to self-completion
factors. In this way, the level of reciprocal self-disclosure increases as the level of intimacy rises
but starts to decline beyond a certain level of intimacy.
5
In this way, using a tool of economics, we provide an explanation for Altman and Taylor
(1973)’s social penetration theory with a focus on the results of “reciprocal self-disclosure.”
The remainder of this paper proceeds in five sections. Section 2 covers self-disclosure in detail, and Section 3 introduces the basic model. We initially focus on self-disclosure communication
when there is no prior communication. In Section 4, we consider the case of using a prior communication (“cue communication”) before starting a self-disclosure. Section 5 concludes the paper.
2
Self-Disclosure
2.1
The costs and benefits of self-disclosure
Generally, a person builds up an intimate relationship through interaction with another party. In
particular, the exchange of private personal information between the two parties plays an important
role in the process of increasing intimacy in a personal relationship. This kind of disclosure of
private personal information is called “self-disclosure” (Altman and Taylor 1973, Daibo et al.
1989, Ando 1994). Self-disclosure affects the individual in the following ways:
(B1) Expression: Expressing and diffusing conflict, uncertainty, and pent-up emotions has a
cathartic effect.
(B2) Self-clarification: Putting one’s own problems and emotions into words requires organization. Further, verbalization can clarify chaotic problems and emotions.
(B3) Social validation: One can receive a range of social supports and feedback from the confidant. Self-understanding can be deepened when ”blind spots” are brought to a person’s
attention.
(B4) Relationship development: The mutual disclosure of various hidden personal aspects prompts
feelings of intimacy and trust.
The above are beneficial components of self-disclosure. Specifically, (B1) and (B2) are effects
arising from the act of self-disclosure itself, independent of the other party’s behavior. On the other
6
hand, (B3) and (B4) are effects initially obtained from feedback to the sender about his/her selfdisclosure by the recipient of that disclosure. Thus, the former are known as self-completion effects
and the latter as interaction effects. However, self-disclosure is accompanied by psychological
costs. According to Derlega (1984), the main reasons for hesitation to disclose private information
are as follows.
(C1) Being rejected by the other party
(C2) Being attacked by the other party
(C3) Information being revealed to a third party; being betrayed
(C4) Losing social control
(C5) Becoming aware of one’s own destructive urges
(C6) Losing independence
These psychological costs rise as the content of the self-disclosure deepens. At the same time,
psychological costs (C1)−(C3) in particular are ameliorated as the level of intimacy with the confidant rises. In contrast, the scale of benefits (B1) and (B2) has no relationship with the level of
intimacy because they are independent of the other party.
Thus, self-disclosure is accompanied by both costs and benefits. People tend to weigh these
costs and benefits and naturally select the optimal level of self-disclosure.
2.2
The reciprocity of self-disclosure and the level of intimacy
The concept of “reciprocity” is important in any consideration of self-disclosure. Reciprocity is
the tendency of a recipient of self-disclosure from another party to “return” self-disclosure to that
party.8
8 There
are three psychological models that describe this tendency: (i) The theory of the mediation of trust and
goodwill (Jourard 1959, Jourard and Landsman 1980); (ii) Social exchange theory (the rule that a payment with
value must be repaid with a payment of similar value); (iii) Modeling theory (in deciding how to behave when the
appropriate behavior is not clear, people take their cue from the behavior of the people around them. As a result, if
7
Importantly, Altman and Taylor (1973) found that self-disclosure based on reciprocity also
exists up to a certain level of intimacy, and when intimacy is above that level, self-disclosure based
on reciprocity declines. In other words, in the initial stage of a relationship, many superficial
self-disclosures are exchanged, and in the mid-stage of the relationship, private self-disclosures
are enthusiastically exchanged. However, in the mature stage of the relationship, with a stable
trust relationship already in place, the importance of reciprocity declines. Psychologists explain
this phenomenon in the mature stage of a relationship as attributable to “loss of the sense of the
necessity of returning self-disclosure for mutual gain.”
In this paper, we will show that this finding with regard to reciprocity can be explained as
resulting from the rational behaviors of the both parties concerned, using an economics model.
3
Basic Model
Upon self-disclosure, the sender and the receiver decide on their respective levels of self-disclosure,
x, y. These indicate both the depth and the breadth of self-disclosure. Both parties gain a payoff
b at each level of self-disclosure from the act of self-disclosure itself, independent of the selfdisclosure of the other party. Further, if the receiver reciprocates the sender’s self-disclosure,
the sender succeeds in creating a trust relationship. Conversely, in returning the sender’s selfdisclosure, the receiver can construct a trust relationship. The sender gains an additional payoff
s > 0 from each unit of trust relationship created. On the other hand, in responding to the sender’s
self-disclosure and creating a trust relationship, the receiver gains a payoff rH of α probability or
a payoff rL of 1 − α probability (rH > 0 > rL ). At the point of self-disclosure, the receiver does
not know which payoff will be realized, and the anticipated payoff at the point of self-disclosure
is r̄≡ αrH + (1 − α)rL . Here, α∈ [0, 1] can be interpreted as an indicator of the trust relationship
(level of intimacy) built up thus far. The value of α and the value of rH and rL are well known to
both parties. Here, we define the trust relationship as as a concave function with self-disclosure by
the other party self-discloses deeply, the recipient takes this as a model and returns the self-disclosure). These three
models emphasize that self-disclosure is “payment” to the recipient. There is no consensus regarding the theory that
explains the reciprocity of self-disclosure, but explanations by (i) and (ii) have the most support.
8
the two parties as inputs (as below). Note that x and y are continuous and differentiable. fx and
fxx represent the first- and second-order differentiations by x respectively. The same rule applies
to y. The next equation 10 lists all the assumptions about the functional forms, which are usually
assumed in the economics model.9
f = f (x, y), fx > 0, fy > 0, fxx < 0, and fyy < 0
(1)
Although we do not assume anything about fxy > 0, here, we advance our discussion on the assumption that the two parties’ self-disclosures are complementary in developing a trust relationship, which means fxy > 0. This is because it is a natural assumption that the level of self-disclosure
of the receiver has a positive correlation with that of the sender.
f (0, 0) = 0, f (x, 0) = 0, and f (0, y) = 0
(2)
Equation 2 describes the assumption about the communication breakdown. Self-disclosure is accompanied by psychological costs, such as the risk that the other party will reveal information. We
consider the cost for each level of self-disclosure as
c(α) > 0 and c0 (α) < 0
(3)
Here, we assume that self-disclosure has a positive cost at all levels of intimacy. Thus, the scope
of c(α) is
c(α) ∈ [b, ∞)
(4)
The receiver, having observed the sender’s self-disclosure, decides on his/her own level of selfdisclosure. On the other side, the sender includes that factor in his/her thinking when deciding on
9 In
the economics field, where we assume that a rational person maximizes his or her utility, these assumptions
about the functional forms are the most standard settings. In other words, the trust relationship increases in x or y, but
the degree of the increase is reduced as x or y increases.
9
his/her level of self-disclosure. Thus, the problem is a Stackelberg game led by the sender. On this
occasion, the respective payoffs to each party from self-disclosing are defined as:
US = f (x, y∗ (x))s + bx − c(α)x
(5)
UR = f (x, y)r̄(α) + by − c(α)y
(6)
The receiver, having observed the sender’s self-disclosure, decides on his/her own level of selfdisclosure. The first-order condition (FOC) of the receiver is:
fy (x, y)r̄(α) + b = c(α)
(7)
The left-hand side of Equation 7 shows the marginal benefit when the level of self-disclosure is
raised, and the right-hand side presents the marginal cost. The first term on the left-hand side is the
marginal benefit when an increase in the level of self-disclosure promotes the formation of a trust
relationship. The second term shows the marginal benefit arising from the act of self-disclosure
itself, independent of the other party .10 Note that the sender decides on the optimal level of
self-disclosure with the above behavior of the receiver in mind. The FOC of the sender is:
fx + fy y (x) s + b = c(α)
0
(8)
From the FOCs of Equations 7 and 8, it can be said that:
REMARKS 1: (a) As the degree of intimacy rises, the level of self-disclosure by both parties rises.
(b) For each of the parties, the higher the value placed on the formation of a trust relationship
the higher the respective levels of self-disclosure. (c) The greater the payoff produced by selfdisclosure the higher the level of self-disclosure.
10 Mathematically,
the complementary assumption results in
10
dy
dx
f
= − fyx
> 0.
yy
Proof of (a)
To solve the sender’s optimized behavior in this context using the economics tool, we assume the
standard assumption for the optimization, which means that the SOC is negative. Here, let us
define SOC as Ω.
Ω ≡ fxx + fxy y0 (x) + fyx + fyy y0 (x) y0 (x) + fy y00 (x) s < 0
(9)
Differentiating both the FOCs in Equations 7 and 8 with respect to α, we get:



fyx + fyy y0 (x) r̄
Ω

fyy r̄


fxy + fyy y0 (x) s
∂x∗
∂α
∂y∗
∂α



0
  c (α) − fy (rH − rL ) 
=
 

c0 (α)
Here, we denote the Hessian matrix as |H|. By rearranging and substituting
the Hessian matrix can be rewritten as:
 fyx fyy r̄
 fyx + fyy − fyy r̄
|H| = 

fyx Ω
fxy + fyy − fyy s


 0 fyy r̄ 
= 

Ω 0
dy
dx
(10)
f
= − fyx
into y0 (x),
yy




(11)
= −Ω fyy r̄ < 0
Using the re-formatted Hessian matrix in Equation 11 and Cramer’s Rule, we get:

c0 (α) −

fy (rH − rL ) fyy r̄  −c0 (α) fyy r̄
>0
=
|H|
c0 (α)
0


0
−Ω c (α) − fy (rH − rL )
0
∂y∗
1  0 c (α) − fy (rH − rL ) 
=
>0

=
∂α
|H| Ω
|H|
c0 (α)
∂x∗
1 
=

∂α
|H|
(12)
(13)
Q.E.D.
11
Proof of (b)
Similarly, using the expression in Equation 11, we get the following for the impact of s on x∗ and
rH (or rL ) on y∗ :


0
fyy r̄ 
fx + fy y0 (x) fyy r̄
fx + fy y0 (x)
1 
∂x∗
=
=
−
>0
=


∂s
|H| − f − f y0 (x) 0
−Ω fyy r̄
Ω
x
y


∂y∗
1  0 − fy α  −Ω fy α
=
>0

=
∂rH
|H| Ω
|H|
0


∗
1  0 − fy (1 − α)  −Ω fy (1 − α)
∂y
=
>0

=
∂rL |H| Ω
|H|
0
(14)
(15)
(16)
Q.E.D.
Proof of (c)
Similarly, using the expression in Equation 11, we get the following for the impact of b on x∗ and
y∗ :


1  −1 fyy r̄  fyy r̄
∂x∗
=
>0

=
∂b
|H| −1 0
|H|


∗
∂y
1  0 −1 
Ω
=
>0

=
∂b
|H| Ω −1
|H|
(17)
(18)
Q.E.D.
REMARKS 1(a) is tantamount to Altman and Taylor (1973)’s process of social penetration, which
states that, as the level of intimacy deepens, self-disclosure progresses from the shallow to the
deeper aspects of personality. However, the reason for raising the level of self-disclosure because
of a rise in intimacy is slightly different between the two parties. From the formula
∂x∗
∂α ,
the sender
raises his/her level of self-disclosure because the increase in intimacy reduces the marginal cost of
self-disclosure. In contrast, an increase in the level of intimacy for the receiver signifies a rise in
12
the trustworthiness of the sender, and he/she raises the level of self-disclosure through i) a rise in
the anticipated payoff from the formation of a trust relationship and ii) a reduction in the marginal
cost of self-disclosure. Regarding REMARKS 1(b), the higher the payoff to each party the higher
the level of self-disclosure, which is highly intuitive. REMARKS 1(c) concerns the impact of
a payoff obtained from the act of self-disclosure independent of the other party’s self-disclosure
(e.g., benefit through self-clarification). The increase in b, which is common to both parties, raises
the levels of self-disclosure from both parties. It is expected that the higher the benefit of this kind
of self-disclosure the more both parties self-disclose, but the type of self-disclosure becomes more
independent between both people in this case.
3.1
Communication Breakdown
Up to here, the premise has been that the receiver reciprocates self-disclosure but, intrinsically,
neither party is likely to self-disclose if there is no positive payoff from self-disclosing. Thus,
from now on, our thinking is conditional upon self-disclosure being likely to occur without prior
cue communication. The sender self-discloses when the payoff s > 0 from the formation of a trust
relationship is great enough to give a non-negative maximized anticipated payoff (US∗ ≥ 0). To
word it the other way around, because he/she believes that the other party is trustworthy enough
that there will be no loss from talking, the sender self-discloses first. However, for the receiver,
responding with self-disclosure is accompanied by risk. For the receiver to self-disclose, the condition UR∗ ≥ 0 must be fulfilled. Hence, the following REMARKS 2:
REMARKS 2:Where the receiver is uncertain of the trustworthiness of the sender, if the level of
intimacy is α∗ ≡
−rL
rH −rL
or less, there is a breakdown in self-disclosure communication.
Proof
Here, we define α, whereby the anticipated payoff (r̄) becomes zero, as α∗ , which is expressed in
the following equation:
r̄(α∗ ) ≡ α∗ rH + (1 − α∗ )rL = 0
(19)
13
As a preparation, if Equation 7 is substituted into b in Equation 6, the receiver’s maximized anticipated payoff is:
UR∗ = f (x∗ , y∗ )r̄(α) + by∗ − c(α)y∗
(20)
By the assumption of f (x, 0) = 0, if the receiver chooses not to reciprocate (i.e., chooses y = 0), the
first term in Equation 21 becomes zero, and the latter two terms in Equation 21 also become zero,
which means that y = 0 brings UR = 0. Therefore, if UR∗ is positive, the receiver chooses an interior
solution of y∗ > 0. Anticipating this, as long as the US∗ is positive, the self-disclosure by each party
is realized. This equilibrium can happen only for α > α∗ , where r̄ is positive. This is because, by
the definition of α∗ , for any α < α∗ , r̄ is negative, which means that by the assumption of c(α) ≥ b,
the receiver’s payoff is negative for any y when he/she participates this communication. Thus, the
receiver chooses y∗ = 0, and the sender, anticipating this behavior, chooses x∗ = 0, thereby resulting in a breakdown in self-disclosure communication. Furthermore, when α = α∗ , we have r̄ = 0;
thus, by the assumption of c(α) ≥ b, the receiver’s payoff is, at most, zero for any y.11 Therefore,
the receiver’s best response is to choose y∗ = 0 and the sender anticipating this behavior will choose
x∗ = 0, which results in a breakdown in self-disclosure communication.
3.2
Q.E.D.
Payoff
Next, for the region of α where the communication occurs (i.e., when α > α∗ ), we see the maximized level of UR∗ as a function of α and differentiate the receiver’s anticipated payoff with respect
to α.
dUR∗ (α)
∂x∗
= fx
r̄ + f (x∗ , y∗ )(rH − rL ) − c0 (α)y∗ > 0
dα
∂α
(21)
Therefore, when α > α∗ , a rise in the level of intimacy boosts the overall anticipated payoff for
the receiver, owing to the following three effects: (1) A rise in the level of self-disclosure by the
11 The
first term in Equation 21 becomes zero and the summation of the latter two terms is zero or less for any y.
14
sender contributes to establishing a trust relationship; (2) because of an increase in the anticipated
payoff, the predicted value of fostering a trust relationship directly rises; and (3) reduction in the
psychological cost accompanying self-disclosure has a positive impact. In Equation 21, the order
of the terms corresponds to each effect above.
3.3
Reciprocity
We now return to the concept of reciprocity of the amount of self-disclosure. From Equation (7),
marginal benefits obtained by increasing the level of self-disclosure can be classified as gains obtained from the formation of a trust relationship and gains arising from the act of self-disclosure independent of the other party. The reciprocity of self-disclosure means that “because self-disclosure
by the other party works as a payment, by also self-disclosing oneself, one repays the other party”.
Therefore, when the gain from self-disclosure is b, which is independent of the other party, the
self-disclosure no longer benefits the other party and is no longer reciprocal in nature. Thus, we
define the reciprocal ratio of self-disclosure within the marginal benefit as “a proportion that is
able to contribute to the other party as well’.
P(α) ≡
fy r̄
fy r̄ + b
(22)
Using the FOC of the receiver, Equation 22 can be written as:
P(α) = 1 −
b
c(α)
(23)
REMARKS 3:(a) As the level of intimacy rises, the reciprocal element of self-disclosure weakens.
(b) When the level of intimacy is low, reciprocal self-disclosure increases as the level of intimacy
rises, but beyond a certain level of intimacy, it begins to decline.
15
Proof of (a)
Differencing P with respect of α yields:
dP(α) bc0 (α)
=
<0
dα
c(α)2
(24)
The last inequality comes from the assumption that the cost of self-disclosure decreases as the level
of intimacy rises.
Q.E.D.
Proof of (b)
We define the level of reciprocal self-disclosure as the overall level of self-disclosure times the
reciprocal ratio of self-disclosure, as shown below:
b
ŷ ≡ y 1 −
c(α)
(25)
Differentiating ŷ with respective to α yields
∗
∂ŷ
bc0 (α)
∂y
∂x∗
b
0
=
+ y (x)
y+ 1−
∂α
c(α)2
c(α)
∂α
∂α
(26)
When α → α∗ , by REMARKS 2, y → 0. Then, the first term in Equation 26 converges to zero. For
the remaining term, we get:
∗
∗ b
∂y
∂x∗
b
∂y ∂x∗ 0
0
1−
+ y (x)
→ 1−
+ y (x)
>0
c(α)
∂α
∂α
c(α∗ )
∂α α=α∗
∂α α=α∗
(27)
Therefore, the following result holds:
∂ŷ
→ 0 + (+) > 0 as α → α∗
∂α
(28)
16
In contrast, when α → 1, c(α) → b, which can be derived by the assumption about the lower bound
of the cost. Thus, the first term in Equation 26 becomes:
bc0 (α)
c0 (α)
y→
y as α → 1
c(α)2
c(α)
(29)
The second term in Equation 26 becomes:
∗
b
∂y
∂x∗
0
1−
+ y (x)
→ 0 as α → 1
c(α)
∂α
∂α
(30)
Combining the two terms, we get:
∂ŷ
c0 (α)
→
y + 0 < 0 as α → 1
∂α
c(α)
(31)
Note that ŷ(α) is continuous on closed intervals [α∗ , 1], and we have
∂ŷ
∗
∂α |α=α
Then, according to the intermediate value theorem, ∃ α∗∗ ∈ [α∗ , 1] such that
> 0 and
∂ŷ
∂α |α=1
∂ŷ
∗∗
∂α (α ) = 0.
< 0.
Q.E.D.
This is depicted in Figure 1. Because the payoff from the act of self-disclosure is obtained independent of the other party, it does not decline as the level of intimacy rises. In contrast, the cost
of self-disclosure is a decreasing function of the level of intimacy. Therefore, when an individual
decides upon a level of self-disclosure at which the marginal benefit is the same as the margin
cost, the proportion of the overall marginal benefit accounted for by self-completion effects rises
as the level of intimacy increases. This indicates that the tacit aim of self-disclosure as the level of
intimacy rises shifts to self-completion factors.
In this way, the level of reciprocal self-disclosure increases as the level of intimacy rises but
begins to decline beyond a certain level of intimacy. This result is exactly in line with the findings
of Altman and Taylor (1973), Altman (1973), and Won-Doornink (1979, 1985), which means that
there is a curvilinear association between the stage of the interpersonal relationship and the degree
of reciprocity of intimate self-disclosures.
17
4
Cue communication
Until now, the results have shown that individuals do not self-disclose up to a certain level of intimacy. This is because the receiver is uncertain about the trustworthiness of the sender. However,
if neither party self-discloses, a trust relationship will never be fostered. Given that, we consider
the situation when additional communication is carried out before self-disclosure and, having dispelled his/her wariness of the sender, the receiver self-discloses. This type of communication is
defined in Dewatripont and Tirole (2005) as “cue communication”. Although the types of communication examined in their paper are somewhat different from ours, the same logic regarding
cue communication works well in our case: Cue communication as discussed here does not have
deep content, such as self-disclosure, and does not directly contribute to the development of a trust
relationship. Instead, cue communication provides clues as to the trustworthiness of the sender.
Here, the periods spent in innocuous conversation in our modern world, for instance, are time spent
engaged in this type of communication. When cue communication succeeds, the receiver learns
whether the potential payoff from establishing a trust relationship with the sender is rH or rL . This
communication, rather than being aimed at fostering a trust relationship, is intended to allow the
receiver to gain understanding of the sender’s character. Before engaging in cue communication,
the sender does not know what kind of judgment the receiver will make about the value of a relationship with him/her. In other words, even if the sender knows the probability of realizing rH and
rL , he/she does not know which will be realized in practice.
4.1
Communicating technology
For cue communication, we apply the same communicating technology used in Dewatripont and
Tirole (2005): p is the probability of the receiver coming to some kind of a decision regarding the
trustworthiness of the sender. The effort put into cue communication by the sender and receiver
is expressed as xc and yc respectively. For the receiver to come to a about the trustworthiness of
the sender, a cue communication by both parties is required. Given that, we define p(xc , yc ) as a
18
function relating to the level of effort from both parties as
p(xc , yc ) = xc yc
(32)
Therefore, we assume xc , yc ∈ [0, 1]. In this type of communication, unlike in self-disclosure communication, the costs are physical and temporal rather than psychological. We define the cost for
each person as an increasing convex function relating to the level of effort, as follows.
S = S(xc ), R = R(yc ), S0 (1) = R0 (1) = ∞
(33)
where S and R can be continuously differentiated on intervals (0,1). Here, the sender and the
receiver determine their own level of effort for cue communication simultaneously and independently. When a function has been defined, such as Equation 32, strategic complementarities arise
and result in multiple equilibria. In particular, zero-effort equilibrium of xc = yc = 0 always exists.
When there are multiple equilibria, we select the Pareto-dominant one and denote it by (xc∗ ,yc∗ ).
Our initial discussion is based on the assumption that cue communication occurs at any value
for α. We then consider the scope of α, where cue communication can occur in practice. When cue
communication is established, it becomes clear that r = rH or r = rL , and so the receiver does not
take the chance of self-disclosing when r = rL < 0.12 Therefore, when cue communication occurs,
only when it is clear that r = rH do the parties move on to the self-disclosure communication specified in the previous section. Thus, with the same utility settings, when the receiver has interpreted
from cue communication that r = rH , the self-disclosure level of both parties is determined as:
x∗ = argmax f (x, y(x))s + bx − c(α)x
(34)
x
y∗ = argmax f (x, y)rH + by − c(α)y
(35)
y
is because if self-disclosure occurs when r = rL < 0, then it follows that UR∗ ≡ f (x∗ , y∗ )rL + by∗ − c(α)y∗ < 0
by the assumption stated in the formula 4.
12 This
19
The only difference from the previous section is that r̄ is replaced by rH in Equation 35. Solving
the relevant FOCs, we set the maximized anticipated payoffs, respectively, as US∗ , UR∗ .
US∗ ≡ f (x∗ , y∗ (x∗ ))s + bx∗ − c(α)x∗ > 0
(36)
UR∗ ≡ f (x∗ , y∗ )rH + by∗ − c(α)y∗ > 0
(37)
Considering payoff, the sender and receiver determine the level of effort they will each put
into cue communication. For both parties to obtain payoffs US∗ , UR∗ , the receiver must perceive
that r = rH . Therefore, we multiply the potential payoff from self-disclosure by the probability α
of this perception occurring. Thus, the respective anticipated payoff from cue communication for
each party is:
USc (xc , yc ) = xc yc αUS∗ − S(xc )
(38)
URc (xc , yc ) = xc yc αUR∗ − R(yc )
(39)
Both parties engage in cue communication with the level of effort that maximizes Equations 38
and 39 above. Each FOC is:
4.2
S0 (xc∗ ) = yc∗ αUS∗
(40)
R0 (yc∗ ) = xc∗ αUR∗
(41)
Payoff
When we differentiate the receiver’s anticipated payoff with respect to α, we arrive at
∂URc∗
∂xc∗
∂U ∗
c∗
= x +
α yc∗UR∗ + xc∗ yc∗ α R > 0
∂α
∂α
∂α
∗
∗
∂U
∂x
where R = fx
rH − c0 (α)y > 0
∂α
∂α
20
(42)
When cue communication occurs, the relationship between the level of intimacy and the anticipated payoff is affected. That is, when the level of intimacy increases, the overall anticipated
payoff for the receiver rises, owing to four effects: (i) The probability of self-disclosure increases
as it becomes more likely that his/her perception will be r = rH , which directly increases the anticipated payoff. (ii) The level of effort expended by the sender on cue communication rises, thereby
increasing the probability of success in the communication and indirectly increasing the anticipated
payoff. (iii) The level of self-disclosure by the sender rises and helps foster a trust relationship,
thereby increasing the payoff from self-disclosure. (iv) The psychological cost of self-disclosure
declines, which increases the self-disclosure payoff. Each term in Equation 42 corresponds to each
channel.
Similarly, we differentiate the sender’s anticipated payoff with respect to α:
∂USc∗
∂U ∗
∂yc∗
c∗
= y +
α xc∗US∗ + xc∗ yc∗ α S > 0
∂α
∂α
∂α
∗
∗
∂U
∂y
where S = fy
s − c0 (α)x > 0
∂α
∂α
(43)
As when the level of intimacy increases, the overall anticipated payoff for the sender rises, owing
to the following four effects: (i) The probability of self-disclosure by the receiver increases as it
becomes more likely that his/her perception will be r = rH , directly increasing the anticipated payoff (yc∗ xc∗US∗ ). (ii) The level of effort expended by the receiver on cue communication rises, which
increases the probability of success in the communication, thereby indirectly boosting the anticic∗
pated payoff ( ∂y∂α αxc∗US∗ ). (iii) The level of self-disclosure by the receiver rises and contributes
∗
to the fostering of a trust relationship, increasing the payoff from self-disclosure (xc∗ yc∗ α fy ∂y
∂α s).
(iv) The psychological cost accompanying self-disclosure declines, increasing the payoff from
self-disclosure (−xc∗ yc∗ αc0 (α)x).
21
4.3
No Cue Communication V.S. Cue Communication
In Section 4, our discussion has progressed on the assumption that cue communication will definitely occur; however, intrinsically, the parties concerned can decide (i) whether to self-disclose
after engaging in cue communication and (ii) whether to self-disclose without cue communication.
Below, we look at the circumstances in which cue communication proceeds and breaks down.
Here, we define α̂ as the minimum levels for α that satisfy URc∗ (xc∗ (α), yc∗ (α)) ≥ 0 and USc∗
(xc∗ (α), yc∗ (α)) ≥ 0. Since having more options should not work to reduce payoffs, we can safely
assume that α̂ < α∗ .13 In other words, we might improve our payoff using cue communication.
Furthermore, we define the level of α that satisfies the following as α̃:
USc (rH ) = xc yc α̃US∗ (rH ) − S(xc ) = US∗ (r̄(α̃))
(44)
Note that α∗ < α̃ because r̄(α̃) > 0. Thus, for α > α̃, the intimacy level is high enough for the
sender to skip the cue communication procedure. When α∗ < α < α̃, although the receiver does not
experience a loss even if he/she self-discloses while still uncertain about the trustworthiness of the
sender, the uncertainty is not very low. Therefore, the gain is greater for the sender if he/she boldly
engages in cue communication so that the receiver may come to believe that r = rH and, thus,
self-disclose at a high level. In this case, the sender attempts to engage in cue communication to
elicit high-level self-disclosure from the receiver. Thus, sometimes cue communication is intended
to elicit a higher level of self-disclosure when the receiver already has an incentive to self-disclose.
For α ≤ α̂ < α∗ , we get URc∗ (xc∗ (α), yc∗ (α))< 0 or/and USc∗ (xc∗ (α), yc∗ (α)) < 0. Thus, the cue
communication breaks down. In addition, from α ≤ α∗ and REMARKS 2, even a self-disclosure
without a cue communication does not occur.
For α̂ < α ≤ α∗ , we get URc∗ (xc∗ (α), yc∗ (α))≥ 0 and USc∗ (xc∗ (α), yc∗ (α)) ≥ 0, thus the cue
communication occurs. Only when the information about the sender turns out to be rH , do they
move forward to a self-disclosure. Since α ≤ α∗ , a self-disclosure without a cue communication
13 It
is true that α̂ = α∗ is theoretically possible, but we differentiate the two criteria for simplicity.
22
never occurs.
For α̂ < α∗ < α < α̃, the receiver does not experience a loss even if he/she self-discloses while
still uncertain about the trustworthiness of the sender. Due to α < α̃, the sender still chooses to
undertake the cue communication procedure because the payoff of doing so is still greater than
self-disclosing without a cue communication.
For α̂ < α∗ < α̃ ≤ α, the receiver does not experience a loss even if he/she self-discloses while
still uncertain about the trustworthiness of the sender. Due to α̃ ≤ α, going directly to the selfdisclosure stage is more beneficial for the sender. This situation can be true when r̄ is very high
due to high existing intimacy. This time, in practice, the sender has real authority, and there is a
breakdown in cue communication. This result implies that when the level of intimacy rises as α
approaches 1, cue communication definitely breaks down.
This is consistent with Jourard and Landsman (1980)’s study showing that only 2% of subjects
self-disclose at their first meeting.
5
Conclusion
In this report, we explain the process of two individuals forming a trust relationship from the
perspective of self-disclosure communication. For two people to foster a trust relationship, it is
necessary that they mutually disclose private personal information. However, because such action
is accompanied by costs and benefits, both parties decide on the optimal level of self-disclosure
based on factors such as costs, the existing level of intimacy, and the potential payoff from the
formation of the relationship.
Self-disclosing when the degree of intimacy is below a certain level means the risk to the
receiver that his/her own information will be revealed by the other party is high; therefore, the
receiver does not reciprocate the sender’s self-disclosure. Anticipating this, the sender has no
incentive to self-disclose; thus, self-disclosure does not occur without prior communication. In
this kind of circumstance, the sender engages in cue communication before self-disclosure so that
23
the receiver comes to see the sender as trustworthy. In contrast, when there is already a certain
level of trust between the two parties, the receiver reciprocates the self-disclosure, even though
the sender’s trustworthiness is still a slight risk because the benefits of self-disclosure outweigh
the costs. Aware of this, the sender self-discloses immediately, without going to the trouble of
spending time and physical resources on cue communication. However, when the receiver is very
wary or there is a high degree of uncertainty surrounding the trustworthiness of the sender, the
sender sometimes attempts to engage in cue communication to elicit a high level of self-disclosure
after becoming trusted, rather than just seeking reciprocal self-disclosure.
The higher the level of intimacy between the two parties, the more frequently self-disclosure
with deep content occurs. At the same time, there is a change in the nature of the self-disclosure. In
other words, as the level of intimacy rises there is a greater focus on the self-completion aspects of
self-disclosure, such as “autocatharsis”, rather than on the aspect of “fostering a trust relationship”.
The behavioral trends observed in the experiments are all explainable in the economics model
constructed in this paper.
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26
Figure 1: Reciprocal self-disclosure and intimacy level
Note: When the level of intimacy is low, as the level of intimacy rises, reciprocal self-disclosure increases, but beyond
a certain level of intimacy it starts to decline.
27