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

5. 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

7. 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

8. 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

9. Predictions of the “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

10. 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

11. Behavior in the Investment Game

12. Definitions
Self-regarding (or “economic man”) preferences are characterized by positively monotonic utility for one’s 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 one’s own or others’ material payoffs
Altruistic preferences are characterized by utility that is monotonically increasing in others’ material payoffs and one’s own payoffs

13. Definitions (cont.)
(direct) Positive reciprocity is a motivation to adopt a generous action that benefits someone else, at one’s own material cost, because that person’s 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 one’s own utility if the other person defects

14. Definitions (cont.)
(direct) Negative reciprocity is a motivation to adopt an action that harms someone else, at one’s own material cost, because that person’s 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

15. 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

16. Comparison of the Amounts Sent in Treatments A and B

17. Comparison of the Amounts “Returned” in Treatments A and C

18. 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

19. 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

20. 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

21. 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

22. 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

23. Models of Other-regarding Preferences
Inequality aversion models (Fehr & Schmidt, QJE, 1999; Bolton & Ockenfels, AER, 2000): utility is increasing with one’s own money payoff but decreasing with the difference between one’s own and others’ money payoffs
Quasi-maximin model (Charness & Rabin, QJE, 2003): utility is increasing with an agent’s own money payoff, with the lowest of all agents’ payoffs, and with the total of all agents’ payoffs

24. Alternative Model Motivated by Data
Egocentric altruism model (Cox & Sadiraj): other-regarding preferences characterized by monotonicity, convexity, and egocentricity

25. 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

26. Prediction of the Fehr-Schmidt Model

27. Prediction of the Bolton-Ockenfels Model

28. Behavior in Experiment 1

29. 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

30. The Quasi-Maximin Model

31. Direct Tests of Quasi-Maximin
Experiment 2
m y1 y2 y3

32. Direct Tests of Quasi-Maximin (cont.)
Experiment 3
m y1 y2 y3

33. Subjects’ Choices in Experiments 2 and 3

34. 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

35. 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)

36. Choices in Experiments 1 and 4

37. 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?

38. With a Model of Egocentric Altruistic Preferences

39. The Two-Agent Egocentric Altruism Model

40. Properties of the Model
Monotonicity
Convexity
Egocentricity
Two Agent Special Case of Egocentricity:
for all

41. 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

42. The Model is Robust
The model can also rationalize behavior in experiments with:
Proposer competition
Responder competition
Voluntary contributions to public goods

43. Incorporating Intentions in 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

44. Reciprocity and Status
We assume
where:
r is a “reciprocity variable”
s is a “status variable”

45. Definition of r
where m(x) is the max. payoff for the second mover, given the first mover’s choice x
and is m(x) when x is neutral

46. Definition of s
where and are the status of the first and second movers in the context of the game currently played

47. 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:

48. Model Assumption that is Tested
A.3  (r, s) is weakly increasing in r and s

49. 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

50. 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

51. 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

52. 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

53. Applications of the Model
Stackelberg duopoly game data
Stackelberg mini-game data

54. .
SUMMARY
CONCLUSIONS

55. Behavior in Fairness Games Exhibits
Unconditional altruism: “others’ payoffs matter”
Trust and fear: “beliefs matter”
Reciprocity: “intentions matter”

56. 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

57. Modeling Fairness Games
Behavior is not generally characterized by:
Inequality aversion
Maxi-min
Efficiency

58. 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

59. 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

60. 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
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.