Trust Signaling
Maroš Servátka (University of Canterbury, NZ)
Steven Tucker (University of Canterbury, NZ)
Radovan Vadovič (ITAM, Mexico)
June 2007
ESA, Rome
What is Trust?
• Defined by Cox [2000]:
– An agent undertakes an action that exhibits trust if the
chosen action:
• creates a monetary gain that could be shared with another agent;
• exposes him to the risk of a loss of utility if the other agent defects
and appropriates too much or all of the monetary gain.
• Trust is a phenomenon present in many economic
and social activities, and in certain scenarios, the
presence of trust allows for mutually better
outcomes.
– For example: trade transactions, investment,
employment, relationships (marriage, friendship, etc).
• Large body of literature exploring various
aspects of trust to explain the deviations from
conventional game theoretic prediction.
• There is no uniformly accepted theory about
what trust is and how it originates.
• Several models attempt to explain trust as a
product of rational behavior
– Falk and Fischbacher, 2006 - reciprocity story
– Battigalli and Dufwenberg, 2007 - guilt aversion story
– Sliwka, forthcoming - conformist-types story
Objective of this study
• To explore strategic implications of trust
• Research questions:
– Can investor strategically signal trust?
– Does trust signaling pay off?
• Investor can invest because he is a trusting
person
– Believes that most people are fair thus expects the
entrepreneur to split the surplus fairly
– Belief about the proportion of fair individuals in
population is purely subjective and summarizes own
experiences and biases
• Investor could be a non-trusting person but still invest
– Belief about the proportion of fair people is not high enough to
induce investment
• Believes many people are selfish and would keep the whole surplus
– However, he is aware of the fact that some selfish entrepreneurs
could interpret investment as a sign of trust and reward this trust
with a fair split.
• Thus, if he invests, his chances of receiving a fair split rise due to
the proportion of selfish entrepreneurs who reward trust.
• These people added to the small proportion of fair people provide
sufficient incentives to invest.
• The reason: objective of the entrepreneur is not to match his initial
belief, but the updated belief that takes into account the amount
invested.
Theoretical background
• We adopt the view of Battigalli and Dufwenberg (2007)
who interpret trust in the framework of guilt-aversion.
• This story has already received some empirical support
in experimental studies of
–
–
–
–
Dufwenberg and Gneezy (2002)
Charness and Dufwenberg (2006)
Schnedler and Vadovič (2007)
Dufwenberg, Servátka, and Vadovič (in progress)
• Allows for introducing strategic considerations of trust in
a tractable way.
Guilt aversion
• If the entrepreneur is guilt-averse, then he experiences a
disutility from “hurting the investor”.
– Hurting = returning to the investor less than expected
– Notice, the entrepreneur’s utility depends upon the investor’s
expectations of his actions.
• To avoid guilt, the entrepreneur optimally splits the
surplus in a way that matches his belief about the
expectations of the investor.
• Therefore, an untrusting investor will invest only if he is
confident that the entrepreneur holds sufficiently high
belief about his expectations.
Modified investment game
Player A (Investor)
t
10
0
Player B (Entrepreneur)
ZERO
HALF
10 – t
10 – t + 3t/2
3t
3t/2
• Player B observes t prior to making his
decision.
– Player’s B belief about the share expected
by player A should depend on t.
– Higher t signals a stronger belief in receiving
a fair share of the surplus.
– The incentives of a guilt-averse player B to
split the surplus fairly should grow in t.
• The crucial element in this logic is that
investment is used as a credible
commitment device.
– The greater t, the greater the loss to player A
if the player B decides to keep everything.
– Because of such credible exposure, it should
be unambiguous that player A has a high
expectation.
– Hence, player B should revise his belief
upwards and then split the surplus fairly to
avoid feeling guilty.
Experimental design
• Two treatments:
– Sequential (SEQ)
• Allows for trust signaling and updating beliefs
• Inherent beliefs might matter
– Simultaneous (SIM)
• Displayed trusting behavior purely reflects subjects' inherent
beliefs about the proportion of fair individuals in the
population
• The difference between these two treatments
will measure the importance of strategic use of
trust.
Predictions: Decisions
• Assumption: player B is guilt averse
– Guilt aversion: If B’s belief about what A expects of
him is high enough, B will return HALF.
• SEQ: t is observable
– A is able to communicate how certain he is about receiving HALF.
– B observes t and updates his belief about A’s belief:
• if B observes t=10, beliefs (about A’s beliefs) are updated upward
• if t=0, beliefs (about A’s beliefs) are updated downward
– Given that B is sufficiently guilt averse, the updated high belief makes it
optimal for B to chose HALF
 A should be confident to invest t=10.
 OUTCOME: player A signals high expectations to player B who matches
these expectations by choosing HALF, i.e., (t=10, HALF)
Predictions: Decisions
• SIM: t is unobservable
– Both players face uncertainty about their respective
beliefs.
• No mechanism for player B to update his beliefs
– Each player's belief is subject to own experiences and
biases.
Theory predicts four outcomes:
• (t=0, ZERO), (t=0, HALF), (t=10, ZERO), (t=10, HALF)
• Average amount invested in SEQ > SIM
• Frequency of HALF in SEQ > SIM
Predictions: Beliefs
• Prior beliefs in SEQ vs. SIM
– Beliefs ASEQ > Beliefs ASIM
– Beliefs BSEQ > Beliefs BSIM
• Conditional Beliefs
– Beliefs ASEQ |t=10 > Beliefs ASEQ |t<10
– Beliefs BSEQ |HALF > Beliefs BSEQ |ZERO
Subjects’ decisions
• Testing classical self-regarding prediction: (t=0, ZERO)
SEQ (n=41)
SIM (n=37)
# of t = 0
5
(12%)
4
(11%)
# of ZERO
21
(51%)
27
(73%)
 The subgame perfect equilibrium for self-regarding
players does not find much support.
Subjects’ decisions
• In Sequential Treatment:
– 21 (51%) players A invested t=10
– 20 (49%) players B returned HALF.
Not strong support for theory of trust signaling.
• In Sequential Treatment, (given that Player A
invested t=10):
– 19 (90%) players B returned HALF
Strong support for trust signaling in terms of decisions made.
Frequency of returning HALF for given t
1
0.9
0.8
0.7
Frequency
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
Investment Level
6
7
8
9
10
Subjects’ decisions
• In Simultaneous Treatment:
–
–
–
–
4 (11%) players A invested t=0
9 (24%) players A invested t=10
27 (73%) players B returned ZERO.
10 (27%) players B returned HALF.
outcome
# of consistent
observations
% consistent
observations conditional
on player A
t=0
ZERO
t=0
HALF
t=10
ZERO
t=10
HALF
4
0
8
1
100%
-
89%
11%
Subjects’ decisions
• Players A invested significantly more in SEQ than SIM
– Mean tSEQ = 6.59, mean tSIM = 5.22
– Mann-Whitney 1-sided: p=0.046
• In SEQ, 21 out of 41 (51%) invested t=10
• In SIM, 9 out of 37 (24%) invested t=10
 Support for Trust Signaling theory
• Players B returned HALF significantly more frequently in
SEQ than SIM
– SEQ: 20 out of 41 (49%) return HALF
– SIM: 10 out of 37 (37%) return HALF
• Fisher exact 1-sided: p=0.04
 Support for Trust Signaling theory
Subjects’ beliefs
• We elicited prior beliefs in a salient way
(Dufwenberg and Gneezy, 2002)
– Subjects in SEQ know that they will play the game in
SEQ. Thus know that they will be dealing with
updated beliefs once players B learn the decision of
their counterpart.
– The prior in SEQ internalizes the fact that B’s update
their beliefs and should therefore be different than in
SIM.
– So we measure prior expectations of updated beliefs
of B’s, i.e., indirectly measure updated beliefs.
Subjects’ beliefs
• Beliefs analysis provides further support for trust
signaling.
– Test for consistency of beliefs
• Beliefs ASEQ (50.63%) = Beliefs BSEQ (50.73%)
– Players’ A beliefs are not different from actual choices
(p=0.78) nor from players B beliefs (p=0.81).
• Beliefs ASIM (46.49%) = Beliefs BSIM (37.32%)
– Players A beliefs are significantly higher than actual choices
(p<0.01), but not different from players B beliefs (p=0.13).
Subjects’ beliefs
• Test for trust signaling
– Beliefs ASEQ (50.63%) > Beliefs ASIM (46.49%)
Weak support for the theory since the direction is correct, but
not significantly different (p=0.264).
– Beliefs BSEQ (50.73%) > Beliefs BSIM (37.32%)
• Players B beliefs in SEQ are significantly greater than SIM
(p<0.01)
Strong support for the theory
Subjects’ beliefs
• Conditional beliefs
– Beliefs ASEQ |t=10 > Beliefs ASEQ |t<10
• (p<0.01 )
– Beliefs BSEQ |HALF > Beliefs BSEQ |ZERO
• (p=0.058)
Updated beliefs in SEQ
• To verify that subjects indeed update beliefs we
measured their beliefs in another treatment after
player B had observed t (n=41)
• We find that:
– Updated beliefs BSEQ |t=10 are greater than updated
beliefs BSEQ |t<10 at p<0.001
– Players B update their beliefs up (to 59%) if t=10 and
down (to 33%) if t<10
Conclusions
• Many subjects strategically signal trust in our
setting
• Their counterparts reward trust
• Theory of trust signaling is supported by both
choices and saliently elicited beliefs
• Further evidence on guilt aversion