An Experiment on Trust in Triads

1
An Experiment on Trust in Triads

• Werner Raub
• Workshop on Social Theory, Trust, Social
  Networks, and Social Capital IINational
  Chengchi University NCCUApril 2011

2
Trust by Example I

• July 18, 2007 end date to purchase a copy of the
  first edition of Theory of Games and Economic
  Behavior by John von Neumann and Oskar
  Morgenstern at eBay from the seller
  bibliomonster for US- 1,900.00. The item had a
  fixed price listing (eBays Buy It Now option)
  and could only be purchased without bidding in an
  auction. Item description Bound in original
  publishers red cloth a bit rubbed at head of
  spine. Black (ink?) mark on top board. Minor
  shelf wear, else very good. Internally, clean and
  free of ink, marginalia and soiling. No dogeared
  pages or tears. Includes the often missing
  corrigenda leaf. A nice, collectable copy.

3
Trust by Example II

• A potential buyer at eBay has to decide whether
  to buy the rare first edition of a book offered
  by a seller and to send the money
• The seller, after receiving the money, has to
  decide whether or not to ship the book to the
  buyer
• If the seller ships and the book corresponds with
  the specifications, both buyer and seller are
  happier after the deal than before the deal
• If the seller does not ship the book, he can try
  to sell it again, while the buyer has lost her
  money

4
The Trust Game
5
Outline

1. Theory and hypotheses on embedded trust
2. Design of the experiment
3. Results
4. Related findings from other empirical studies
   using complementary research designs
5. Conclusions ongoing and future research

6

• Theory and Hypotheses on
• Embedded Trust

7
Embedded Trust

• Trust problems (and other social and economic
  interactions) are often embedded in the sense
  of
• repeated transactions between the same actors
• actors encounter and exchange information with
  partners of their partner
• ? need to extend predictions for trust situations
  to embedded settings (trust in networks)

8
Embeddedness Mechanisms
Dyadic embeddedness Network embeddedness
Learning Common history of past interactions information about the partner from own experiences Information from third parties about their past experiences with the partner
Control Expected future interactions opportunities for conditional cooperation via, e.g., tit for tat Opportunities for conditional cooperation involving third parties voice (reputation effects)

9
Approach

• We distinguish between different embeddedness
  effects
• theoretically
• empirically
• We consider games on networks and neglect
  strategic network formation embeddedness is
  exogenous in the experiment (but see concluding
  discussion)
• We focus on trust as a result of enlightened
  self-interest and neglect (more or less)
  non-selfish utility

10
Theories for Deriving Hypotheses on Embeddedness
Effects
Dyadic embeddedness Network embeddedness
Learning Adaptive learning models information diffusion models Adaptive learning models information diffusion models
Learning and control Models for repeated games with incomplete information Models for repeated games with incomplete information
Control Models for repeated games with complete information Models for repeated games with complete information
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Trust in Finitely Repeated Games with Incomplete
Information Intuition I

• Consider a finitely repeated Trust Game with a
  trustee who, with some positive (and possibly
  very small) probability, has no incentive to
  abuse trust in a one-shot Trust Game (e.g.,
  inequity aversion)
• The trustee may then honor trust for one of two
  very different reasons
• No incentive to abuse trust in a one-shot Trust
  Game
• Reputation building if trust is abused, trustor
  can infer trustees type for sure (learning) and
  may never place trust again (control)
• Trustor may therefore be inclined to place trust

12
Trust in Finitely Repeated Games with Incomplete
Information Intuition II

• Thus
• Trustor tries to learn about and controls the
  trustee, taking the trustees incentives for
  reputation building into account
• Trustee balances long-term effects of his
  reputation and short-term incentives for abusing
  trust, taking into account that the trustor
  anticipates this balancing
• Some properties of the equilibrium
• Trust is placed and honored in early rounds of
  the game
• Actors randomize afterwards
• Placed trust is abused in final rounds of the
  game
• Once abused, trust is never placed again

13
Hypotheses Summary
Dyadic embeddedness Network embeddedness
Learning Trust increases (decreases) with positive (negative) own experiences with the trustee Trust increases (decreases) with positive (negative) information on the trustee received from other trustors
Control Trust and trustworthiness increase with the likelihood of future interactions Trust and trustworthiness increase with the trustors control opportunities through her network with other trustors
14

• Design of the Experiment

15
Lab Experiment

• Subjects play repeated Trust Games in the lab
• Anonymous interactions with actual other subjects
  in the lab
• Complete game structure provided in the
  instructions no deception
• Points earned represent actual money for the
  subjects

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Trust Game in the Lab Experiment


Number of points


A B


right

10

10

A




down


right


0
40

B




down


20

20


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Interaction Structure

• Two trustors play with the same trustee for 15
  rounds (triads)
• In each round, trustor 1 plays first, trustor 2
  second
• Depending on experimental condition information
  exchange about past behavior between trustors

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Two Experimental Conditions

• No information exchange between trustors
• each trustor only knows what happens in her own
  Trust Games with the trustee
• ? opportunity for dyadic learning and control
• ? no opportunity for network learning and
  control
• Full information exchange between trustors
• after each Trust Game, also the trustor not
  involved in that game receives information on the
  choices made in that game
• ? opportunity for dyadic learning and control
• ? opportunity for network learning and control

19
Further Set-Up

• Both conditions subjects know what kind of
  information everybody receives
• Each subject plays three repeated trust games in
  the same information condition once as trustor
  1, once as trustor 2, once as trustee
• Subjects are rematched between the repeated
  games never rematched to other subjects they had
  already played with subjects are informed on the
  rematching process
• Experiment conducted in ELSE lab of UU, using
  z-Tree software
• 72 subjects, i.e., data on 72 triads and 72x15x2
  2160 Trust Games (1080 with and 1080 without
  information exchange between trustors)

20
Lab Experiment andEmbeddedness Effects

• Lab experiment allows to test hypotheses on
  effects of dyadic embeddedness and network
  embeddedness on trust and trustworthiness

21

• Results

22
Three-Level Logistic Regression

• Estimate probability to trust / honor trust
  conditional on past experiences, rounds to go,
  information condition
• Three-level random effects model
• Levels decision trustor triad
• 2160 decisions by 144 trustors in 72 triads
• 1542 decisions by 72 trustees in 72 triads
• Clustering within trustors in different series of
  games neglected
• Trustor level variance is small
• Results are rather robust for the specification
  of random structure

23
Results Effects of Embeddedness on Trust of the
Trustor
144 trustors
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Results Effects of Dyadic Embeddedness on Trust
of the Trustor

• Support for hypotheses on dyadic learning and on
  dyadic control effects on trustor behavior
• Trustors are more (less) likely to trust
• after having experienced more honored (abused)
  trust in own interactions with trustee (dyadic
  learning)
• the larger (smaller) the number of rounds still
  to be played (also strong endgame effect)
  (dyadic control)

25
Results Effects of Network Embeddedness on Trust
of the Trustor

• Evidence for network learning effects on trustor
  behavior trustors are more (less) likely to
  trust after having observed more honored (abused)
  trust in the other trustors interactions with
  the trustee
• No evidence for network control effects on
  trustor behavior no main effect of information
  condition no interaction effect of information
  condition with rounds still to be played
  decrease of trust does not start later in
  condition with full information exchange between
  trustors

26
Results Effects of Embeddedness
onTrustworthiness of theTrustee
72 trustees

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Results Effects of Dyadic Embeddedness on
Trustworthiness of the Trustee

• Support for hypothesis on dyadic control effects
  on trustee behavior
• Trustees are more likely to honor trust the
  larger the number of rounds still to be played
  with the respective trustor
• Also strong endgame effect

28
Results Effects of Network Embeddedness on
Trustworthiness of the Trustee

• Support for hypothesis on network control effects
  on trustee behavior
• Positive effect of full information condition on
  likelihood of honoring trust
• Endgame effect stronger for interactions with
  trustor 2 (who has less control opportunities
  than trustor 1)

29
Puzzle

• Trustee reacts to trustors opportunities for
• dyadic control and
• network control
• ?Trustee seemingly takes reputation effects of
  his behavior into account
• Trustor reacts to her own opportunities for
  dyadic control
• Trustor does not react to her own opportunities
  for network control

30

• Related Findings from Other Empirical Studies
  Using Complementary Research Designs

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Evidence on Embeddedness Effects from
Complementary Research Designs

• Approach use complementary research designs
  (survey, vignette study, lab experiment) for
  multiple tests of the same hypotheses (cf.
  triangulation, cross validation)
• Similar perspective
• Sociology J.H. Goldthorpe (1996) The
  Quantitative Analysis of Large-scale Data Sets
  and Rational Action Theory For a Sociological
  Alliance, ESR 12
• Economics G.W. Harrison J.L. List (2004) Field
  Experiments, JEL 42(4)

32
Alternative DesignsAdvantages and Disadvantages
Advantages Disadvantages
Survey Actual interactions Measurement problems less control over variables
Lab experiment Control over incentives and embeddedness variables Abstract external validity
Vignette study Less abstract than lab experiments control over variables Hypothetical interactions lack of incentive compatibility
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Summary of Empirical Evidence
Survey Vignette study Lab experiment
Dyadic learning Consistent support for dyadic learning and control effects on trust of trustor Quite some support for dyadic control effects on trustworthiness of trustee Consistent support for dyadic learning and control effects on trust of trustor Quite some support for dyadic control effects on trustworthiness of trustee Consistent support for dyadic learning and control effects on trust of trustor Quite some support for dyadic control effects on trustworthiness of trustee
Dyadic control Consistent support for dyadic learning and control effects on trust of trustor Quite some support for dyadic control effects on trustworthiness of trustee Consistent support for dyadic learning and control effects on trust of trustor Quite some support for dyadic control effects on trustworthiness of trustee Consistent support for dyadic learning and control effects on trust of trustor Quite some support for dyadic control effects on trustworthiness of trustee
Network learning Consistent support for network learning effects on trust of trustor No support for network control effects on trust of trustor Consistent support for network control effects on trustworthiness of trustee Consistent support for network learning effects on trust of trustor No support for network control effects on trust of trustor Consistent support for network control effects on trustworthiness of trustee Consistent support for network learning effects on trust of trustor No support for network control effects on trust of trustor Consistent support for network control effects on trustworthiness of trustee
Network control Consistent support for network learning effects on trust of trustor No support for network control effects on trust of trustor Consistent support for network control effects on trustworthiness of trustee Consistent support for network learning effects on trust of trustor No support for network control effects on trust of trustor Consistent support for network control effects on trustworthiness of trustee Consistent support for network learning effects on trust of trustor No support for network control effects on trust of trustor Consistent support for network control effects on trustworthiness of trustee
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Once Again the Puzzle

• Trustee reacts to trustors opportunities for
• dyadic control and
• network control
• ?Trustee seemingly takes reputation effects of
  his behavior into account
• Trustor reacts to her own opportunities for
  dyadic control
• Trustor does not react to her own opportunities
  for network control

35
How (not) to Explain the Puzzle?

• Data and/or measurement problems (including
  sample selectivity and endogeneity of network
  embeddedness) could be (part of) the reason why
  we do not find network control effects on trustor
  behavior in survey data (see Buskens 2002)
• Data and/or measurement problems are much less
  plausible reasons for the lack of network control
  effects on trustor behavior in the experiment

36
How to Explain the PuzzleLimits of Strategic
Rationality?

• General idea Trustor anticipation on her own
  opportunities for network control involves too
  many steps of iterated reasoning, at least for
  inexperienced subjects
• Network control effects on trustee behavior
  require only that trustee anticipates that own
  present behavior affects future trust of the
  present or other trustors
• Network control effects on trustor behavior
  require that trustor anticipates that the trustee
  anticipates on effects of his present behavior on
  future trust of other trustors

37
Similar Arguments in the Literature

• Equilibrium behavior becomes less likely when
  actors have to reason many steps ahead
• Equilibrium behavior requires that actors are
  sufficiently experienced
• (see, e.g., Binmore, Camerer, Kreps)

38

• Conclusions
• Ongoing and Future Research

39
Testable Implications ofthe Explanation of the
Puzzle and Empirical Evidence

• In the experiment, trustors who have been in the
  role of trustee in an earlier game (and thus have
  more experience) should be more likely to react
  to network control opportunities. There is some
  support for this effect in our data.
• We also find support for network control effects
  on trustor behavior in one of our vignette
  studies with experienced subjects (purchase
  managers) in the trustor role.

40
Extended Version of Our Experiment Some
Preliminary Evidence for Experience Effects I

• We meanwhile repeated the experiment with
  subjects playing 6 rather than 3 repeated trust
  games
• Each subject was twice in each role (trustor 1,
  trustor 2, trustee)
• 138 subjects, data on 8.280 trust games
• First question is there evidence for experience
  effects in the sense that behavior in later
  repeated trust games differs from behavior in
  earlier repeated trust games?

41
Extended Version of Our Experiment Some
Preliminary Evidence for Experience Effects II
42
Related Empirical Evidence fromOther Research

• Professionals tend to implement relatively
  complex equilibrium behavior as well as
  equilibrium behavior that requires quite some
  iterated reasoning, also in situations where
  non-professionals fail to do so
• Professional soccer players (versus college
  students) in zero-sum games such as penalty kicks
  (but also strategically equivalent lab
  experiments) Palacios-Huerta Volij Berger
  Hammer
• Chess Grandmasters versus college students in the
  Centipede Game Palacios-Huerta Volij
• Related empirical evidence on spillover effects
  between games (Bednar et al.)

43
Further Extension Investments in Embeddedness
and Strategic Network Formation I

• Embeddedness is exogenous in the experiment
• Consider an alternative scenario before playing
  the repeated Trust Games, subjects themselves
  decide to play in one of the two information
  exchange conditions. Playing in full information
  exchange between trustors is costly
• Thus, the alternative scenario includes strategic
  network formation subjects can invest in network
  embeddedness

44
Further Extension Investments in Embeddedness
and Strategic Network Formation II

• The alternative scenario allows for an analysis
  of strategic network formation under the
  assumption of full strategic rationality
• Questions
• Effects of game parameters (payoffs, of rounds
  of the repeated trust game)?
• Effects of who can invest in network
  embeddedness (trustors or trustee)?

45
Further Extension Investments in Embeddedness
and Strategic Network Formation III

• Theoretical approach
• Calculate expected payoffs in equilibrium for the
  two conditions (no information exchange between
  trustors vs. full information exchange between
  trustors)
• Difference willingness to pay
• Issue possible signaling effects if trustee can
  invest in embeddedness

46

• Thanks for your attention!
• More information
• www.fss.uu.nl/soc/iscore

47

• Additional Slides

48
Further Details on the Experiment

• Sessions took between 55 and 70 minutes.
• Subjects earnings
• Average 10.67
• 10.25 in condition without information exchange
• 11.10 in condition with full information
  exchange
• Minimum earnings 7.00
• Maximum earnings 12.40

49
Comparison of the Design with Bolton et al. 2004
(BKO 04) and Bolton Ockenfels 2009 (BO 09)

• No information exchange between trustors
  resembles the partners market in BKO 04 and BO
  09
• Full information exchange between trustors
  combines dyadic embeddedness and network
  embeddedness and thus differs from the
  reputation market in BKO 04 and BO 09 that
  represents exclusively a form of network
  embeddedness
• BKO 04 and BO 09 has no condition that combines
  dyadic and network embeddedness
• Our experiment neglects the strangers market in
  BKO 04 and BO 09

50
Trust Problems as Social Dilemmas

• The buyer (trustor) has to trust the seller
  (trustee) that he ships the book and that the
  book corresponds with the specifications
• The trustee has an incentive to abuse trust
• This may induce the trustor not to place trust in
  the first place
• Placed and honored trust is better for both
  actors than no trust.
• Hence, trust problems as an example of social
  dilemmas goal-directed behavior leads to poor
  outcomes (unintended consequences)

51
Trust Problems as a Sociological Problem

• Problem of social order
• Trust problems in economic exchange (e.g.,
  buyer-supplier, RD-alliances)
• Trust problems in social exchange (e.g., help
  among friends)

52
Results Effects on Trust
Information condition No net effect
Abused own trust in past -
Honored own trust in past
Abused other trust in past -
Honored other trust in past
Rounds to go
Rounds to go information 0
Round 14 -
Round 15 -
Info cond round 14 0
Info cond round 15 -
53
Results Effects on Trustworthiness
Information condition
Rounds to go
Rounds to go information -
Round 14 -
Round 15 -
Info cond round 14 trustor 2 -
Info cond round 15 trustor 2 -
54
Results Effects on Trust
55
Results Effects on Trustworthiness
56
Results Experience Effects