TRUST, FEAR, RECIPROCITY, AND ALTRUISM: Theory and Experiment James C. Cox University of Arizona and Indiana University

Central Objective of the Research Improve theory through a program of: Experimental testing; and Theoretical modeling motivated by data

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

Parsimony (cont.) Develop an integrated approach to modeling behavior that is: Unconditional on intentions; or Conditional on others’ revealed intentions

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

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

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

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

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

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

Behavior in the Investment Game

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

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

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

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

Comparison of the Amounts Sent in Treatments A and B

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

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

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

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

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

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

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

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

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

Prediction of the Fehr-Schmidt Model

Prediction of the Bolton-Ockenfels Model

Behavior in Experiment 1

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

The Quasi-Maximin Model

Direct Tests of Quasi-Maximin Experiment 2 m y1 y2 y3 10 0 6 6 10 0 15 15 10 0 2 33

Direct Tests of Quasi-Maximin (cont.) Experiment 3 m y1 y2 y3 10 0 15 15 10 3 12 15 10 4 5 21

Subjects’ Choices in Experiments 2 and 3

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

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)

Choices in Experiments 1 and 4

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?

With a Model of Egocentric Altruistic Preferences

The Two-Agent Egocentric Altruism Model

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

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

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

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

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

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

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

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:

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

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

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

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

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

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

. SUMMARY CONCLUSIONS

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

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

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

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

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

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.