TRUST, FEAR, RECIPROCITY, AND ALTRUISM: Theory and Experiment

1
TRUST, FEAR, RECIPROCITY, AND ALTRUISM Theory
and Experiment

• James C. Cox
• University of Arizona
• and Indiana University

2
Central Objective of the Research

• Improve theory through a program of
• Experimental testing and
• Theoretical modeling motivated by data

3
Implications of Parsimony

• Design experiments to identify
• When the economic man model does not predict
  well and models of other-regarding
  preferences are needed
• When the other-regarding preferences need to
  include beliefs and intentions

4
Parsimony (cont.)

• Develop an integrated approach to modeling
  behavior that is
• Unconditional on intentions or
• Conditional on others revealed intentions

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Contents

• Experimental designs that discriminate among
  unconditional altruism, positive reciprocity,
  trust, negative reciprocity, and fear
•  
• Effects of social distance and decision context
  on reciprocal behavior

6
Contents (cont.)

• Direct tests of alternative models
•  
• New models of patterns of behavior that
• (a) are conditional or
• (b) are not conditional on others intentions
  and status

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An Example The Investment Game

• Subjects are paired
• Each subject in each pair is given 10
• Second movers are told to keep their 10
• First movers can either
• Keep their 10 or
• Give some or all of it to the second mover
• Any amount given is multiplied by 3 by the
  experimenter

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Investment Game (cont.)

• Second movers can either
• Keep all of any amount received or
• Return part or all of it to the first mover
• All of the above is common information given to
  all subjects
• The game is played only once

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Predictions ofthe Economic Man Model

• Since second movers care only about their own
  material gain, they will keep any tripled amount
  sent by first movers
• Since first movers care only about their own
  material gain, and know that second movers have
  the same kind of preferences, first movers send
  nothing

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Predictions (cont.)

• Zero returned and sent is the subgame perfect
  equilibrium of this game, given the economic man
  assumption about preferences
• The predicted outcome is inefficient Each
  subject pair is predicted to get 20 in payoff
  just the endowment when it could have gotten as
  much as 40

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Behavior in the Investment Game
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Definitions

• Self-regarding (or economic man) preferences
  are characterized by positively monotonic utility
  for ones own material payoffs and indifference
  about others material payoffs
• Other-regarding preferences are characterized by
  utility that is not constant with respect to
  variations in ones own or others material
  payoffs
• Altruistic preferences are characterized by
  utility that is monotonically increasing in
  others material payoffs and ones own payoffs

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Definitions (cont.)

• (direct) Positive reciprocity is a motivation to
  adopt a generous action that benefits someone
  else, at ones own material cost, because that
  persons intentional behavior was perceived to be
  beneficial to oneself
• Trust is a belief that one agent has about
  another. A trusting action is one that creates
  the possibility of mutual benefit and the risk of
  loss of ones own utility if the other person
  defects

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Definitions (cont.)

• (direct) Negative reciprocity is a motivation to
  adopt an action that harms someone else, at ones
  own material cost, because that persons
  intentional behavior was perceived to be harmful
  to oneself
• Fear is a belief that one agent has about
  another. An action that is fearful of another is
  one that forgoes an otherwise preferred action
  because of a belief that the other agent will
  inflict costly punishment as a response to choice
  of the otherwise-preferred action

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Investment Game Triadic Design

• Treatment A is the investment game
• Treatment B is a dictator game that gives
  dictators the same choices that first movers have
  in the investment game
• Treatment C is a dictator game that gives
  dictators the same choices that second movers
  have in the investment game

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Comparison of the Amounts Sent in Treatments A
and B
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Comparison of the Amounts Returned in
Treatments A and C
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Conclusions about Behavior

• Behavior in the investment game is known to
  exhibit trust because first movers send
• significantly more in the investment game than
  in the first-mover dictator control treatment
• Behavior in the investment game is known to
  exhibit positive reciprocity because second
  movers return significantly more in the
  investment game than in the second-mover dictator
  control treatment

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Implications for Theory

• Data-consistent models of first-mover behavior in
  the investment game must incorporate beliefs
  about others behavior
• Data-consistent models of second-mover behavior
  in the investment game must incorporate others
  intentions

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Conclusions from Many Other Experiments with Game
Triads

• Positive reciprocity is significant in the
  moonlighting game but negative reciprocity is not
  significant
• Trust is significant in the moonlighting game but
  fear is not significant
• Positive reciprocity is significant in the trust
  game with a single blind protocol but not with a
  double blind protocol
• Positive reciprocity in the trust game is
  invariant with a doubling of money payoffs

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Conclusions from Triads (cont.)

• Negative reciprocity and fear are not significant
  in the punishment mini-ultimatum game (MUG)
• Play in the punishment MUG is invariant with
  framing the task as market exchange
• Negative reciprocity is significant in the
  punishment MUG if it is embedded within a context
  of similar games

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Conclusions from Triads (cont.)

• Females are less positively reciprocal in the
  investment game than are males
• Groups are less generous in the investment game
  than are individuals

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Models of Other-regarding Preferences

• Inequality aversion models (Fehr Schmidt, QJE,
  1999 Bolton Ockenfels, AER, 2000) utility is
  increasing with ones own money payoff but
  decreasing with the difference between ones own
  and others money payoffs
• Quasi-maximin model (Charness Rabin, QJE,
  2003) utility is increasing with an agents own
  money payoff, with the lowest of all agents
  payoffs, and with the total of all agents payoffs

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Alternative Model Motivated by Data

• Egocentric altruism model (Cox Sadiraj)
  other-regarding preferences characterized by
  monotonicity, convexity, and egocentricity

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Exp.1 A Direct Test of Inequality Aversion

• This test is provided by the first-mover
  dictator control treatment for the investment
  game triad
• The dictator is given 10
• The anonymously-paired subject is given 10
• The dictator can keep all of his 10 or give any
  integral part of it to the paired person
• Any amount given is tripled by the experimenter

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Prediction of the Fehr-Schmidt Model
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Prediction of the Bolton-Ockenfels Model
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Behavior in Experiment 1
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Behavior in Experiment 1 (cont.)

• 19 of 30 or 63 of the dictators gave positive
  amounts to the other person.
• The average amount given was 3.63
• The average payoff of dictators was 6.37 and the
  average payoff of non-dictators was 20.89

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The Quasi-Maximin Model
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Direct Tests of Quasi-Maximin

• Experiment 2
• m y1 y2 y3
• 10 0 6 6
• 10 0 15 15
• 10 0 2 33

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Direct Tests of Quasi-Maximin (cont.)

• Experiment 3
• m y1 y2 y3
• 10 0 15 15
• 10 3 12 15
• 10 4 5 21

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Subjects Choices in Experiments 2 and 3
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Behavior in Experiments 2 and 3 (cont.)

• The choices of 85 of the subjects in experiment
  2 are inconsistent with quasi-maximin preferences
• The choices of 94 of the subjects in experiment
  3 are inconsistent with quasi-maximin preferences

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More Information about Subjects Preferences

• Experiment 4 differs from experiment 1 only by
  introduction of the opportunity to take money as
  well as give it
• Amounts given are multiplied by 3
• Amounts taken are not transformed
• Amounts taken cannot exceed 5 (first-mover
  control for the moonlighting triad)

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Choices in Experiments 1 and 4
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Behavior Changes Character when the Feasible Set
Changes

• In experiment 1, 67 of dictators gave money to
  others who would, as a result, have significantly
  higher payoffs than the dictators
• In experiment 4, 70 of dictators took money from
  the others who would, as a result, have
  significantly lower payoffs than the dictators
• How can such behavior be explained?

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With a Model of Egocentric Altruistic
Preferences
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The Two-Agent Egocentric Altruism Model
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Properties of the Model

• Monotonicity
• Convexity
• Egocentricity
• Two Agent Special Case of Egocentricity
• for all
  

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Consistency with Data

• The egocentric altruism model is consistent with
  data for
• 100 of subjects in experiments 1 and 4
• 85 of subjects in experiment 2
• 88 of subjects in experiment 3

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The Model is Robust

• The model can also rationalize behavior in
  experiments with
• Proposer competition
• Responder competition
• Voluntary contributions to public goods

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Incorporating Intentionsin a Tractable Way
Note that MRS WTP 1/MRS at an
allocation on the 45 line where m
y Convexity implies higher WTP if and lower
WTP if
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Reciprocity and Status

• We assume
• where
• r is a reciprocity variable
• s is a status variable

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Definition of r

• where m(x) is the max. payoff for the second
  mover, given the first movers choice x
• and is m(x) when x is neutral

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Definition of s

• where and are the status of the
  first and second movers in the context of the
  game currently played

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Assumptions Used in Estimation

• A.1 Individuals choose so as to maximize a
  utility function of the given form
• A.2 The emotional state function ? (r, s) is
  identical across individuals and there is a
  zero-mean idiosyncratic term such that

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Model Assumption that is Tested

• A.3 ? (r, s) is weakly increasing in r and s

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Data Used in Estimating the Model

• Dictator games, with and without a status
  treatment
• Stackelberg duopoly games
• Mini-ultimatum games with variable reference
• payoff conditions
• Ultimatum games with random and earned
• entitlements to be first mover
• Moonlighting games

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Summary Conclusions from Estimation

• The model captures baseline altruism in dictator
  games
• The model explains how status affects altruism in
  dictator games
• The model explains reciprocal responses
• in Stackelberg duopoly games

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Summary Conclusions (cont.)

• The model explains how changing perceptions of
  property rights affect reciprocity in
  mini-ultimatum games
• The model explains the interaction of status and
  reciprocity in ultimatum games
• The model explains reciprocal behavior in
  moonlighting games

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Work in Progress A Nonparametric Model of
Revealed Altruism

• Elements of the Model
• Partial Ordering of Preferences more altruistic
  than (MAT)
• Partial Ordering of Budget Sets more generous
  than (MGT)
• Reciprocity Axiom more generous choices by the
  first mover induce more altruistic preferences in
  the second mover

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Applications of the Model

• Stackelberg duopoly game data
• Stackelberg mini-game data

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.

• SUMMARY
• CONCLUSIONS

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Behavior in Fairness Games Exhibits

• Unconditional altruism others payoffs matter
• Trust and fear beliefs matter
• Reciprocity intentions matter

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Whether Trust, Fear, Reciprocity or Altruism is
Exhibited Depends on

• Single-blind vs. double-blind protocol who is
  observing matters
• Context in which a specific game is embedded
  fairness is a relative concept
• Type of agent
• Group or individual
• Male or female

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Modeling Fairness Games

• Behavior is not generally characterized by
• Inequality aversion
• Maxi-min
• Efficiency

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Modeling (cont.)

• Behavior is characterized by other-regarding
  preferences that are
• Egocentric
• Convex
• Positively monotonic in others payoffs, except
  when they are conditional on intentions

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Modeling (cont.)

• Intentions (reciprocity) and status can be
  incorporated in a tractable model of
  other-regarding preferences
• Individual-subject differences can be
  parsimoniously incorporated in a model of
  other-regarding preferences

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References

• James C. Cox, Trust, Reciprocity, and
  Other-Regarding Preferences Groups vs.
  Individuals and Males vs. Females, in R. Zwick
  and A. Rapoport, (eds.), Advances in Experimental
  Business Research, Kluwer Academic Publishers,
  2002.
• James C. Cox, How to Identify Trust and
  Reciprocity, Games and Economic Behavior, 46,
  no. 2, 2004, pp. 260-281
• James C. Cox and Cary A. Deck, On the Nature of
  Reciprocal Motives, Economic Inquiry,
  forthcoming.
• James C. Cox, Daniel Friedman, and Steven
  Gjerstad, A Tractable Model of Reciprocity and
  Fairness, University of Arizona Discussion
  Paper, 2005.
• James C. Cox and Vjollca Sadiraj, Direct Tests
  of Models of Social Preferences and Introduction
  of a New Model, University of Arizona Discussion
  Paper, 2005.
• James C. Cox, Klarita Sadiraj, and Vjollca
  Sadiraj, Implications of Trust, Fear, and
  Reciprocity for Modeling Economic Behavior,
  University of Arizona Discussion Paper, 2004.