Trust Signaling

Maroš Servátka (University of Canterbury, NZ) Steven Tucker (University of Canterbury, NZ)

Radovan Vadovič (ITAM, Mexico)

June 2007ESA, 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

t

Player A (Investor)

Player B (Entrepreneur)0 10

HALF

10 – t

3t

ZERO

10 – t + 3t/2

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)

The subgame perfect equilibrium for self-regarding players does not find much support.

SEQ (n=41) SIM (n=37)

# of t = 0 5(12%)

4(11%)

# of ZERO 21(51%)

27(73%)

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

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10

Investment Level

Freq

uenc

y

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 t=0ZERO

t=0HALF

t=10ZERO

t=10HALF

# of consistentobservations

4 0 8 1

% consistent observations conditional on player A

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