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Contents 1 Challenges 2 Trust game 3 References 4 Further reading

The dictator game is a very simple game in experimental economics, similar to the ultimatum game. Experimental results in the dictator game have often been cited as a conclusive rebuttal of the rationally self-interested individual (homo economicus) model of economic behavior,^[1] although this conclusion is controversial.^[2]

In the dictator game, the first player, "the proposer", determines an allocation (split) of some endowment (such as a cash prize). The second player, "the responder", simply receives the remainder of the endowment not allocated by the proposer to herself. The responder's role is entirely passive (she has no strategic input into the outcome of the game). As a result, the dictator game is not formally a game at all (as the term is used in game theory). To be a game, every player's outcome must depend on the actions of at least some others. Since the proposer's outcome depends only on his own actions, this situation is one of decision theory and not game theory. Despite this formal point, the dictator game is used in the game theory literature as a degenerate game.

This game has been used to test the homo economicus model of individual behavior: if individuals were only concerned with their own economic well being, proposers (acting as dictators) would allocate the entire good to themselves and give nothing to the responder. Experimental results have indicated that individuals often allocate money to the responders, reducing the amount of money they receive.^[3] These results appear robust: for example, Henrich, et al. discovered in a wide cross cultural study that proposers do allocate a non-zero share of the endowment to the responder.^[1]

If these experiments appropriately reflect individuals' preferences outside of the laboratory, these results appear to demonstrate that either:

1. Proposers fail to maximize their own expected utility, or
2. Proposer's utility functions include benefits received by others.

Additional experiments have shown that subjects maintain a high degree of consistency across multiple versions of the dictator game in which the cost of giving varies.^[4] This suggests that dictator game behavior is, in fact, altruism instead of the failure of optimizing behavior. Other experiments have shown a relationship between political participation and dictator game giving, suggesting that it may be an externally valid indicator of concern for the well-being of others.^[5][6]

[edit] Challenges

Some authors have suggested that giving in the dictator game does not entail that individuals wish to maximize other's benefit (altruism). Instead they suggest that individuals have some negative utility associated with being seen as greedy, and are avoiding this judgment by the experimenter. Some experiments have been performed to test this hypothesis with mixed results.^[7]

Further experiments testing experimental effects have been performed. Bardsley has performed experiments where individuals are given the opportunity to give money, give nothing, or take money from the respondent.^[2] In these cases most individuals far from showing altruism actually take money. And comparing the taking games with dictator games which start from the same endowments, most people who give in the dictator game would take in a taking game. Bardsley suggests two interpretations for these results. First, it may be that the range of options provides different cues to experimental subjects about what is expected of them. "Subjects might perceive dictator games as being about giving, since they can either do nothing or give, and so ask themselves how much to give. Whilst the taking game... might appear to be about taking for analogous reasons, so subjects ask themselves how much to take."^[2] On this interpretation dictator game giving is a response to demand characteristics of the experiment. Second, subjects' behavior may be affected by a kind of framing effect. What a subject considers to be an appropriately kind behavior depends on the range of behaviors available. In the taking game, the range includes worse alternatives than the dictator game. As a result giving less, or even taking, may appear equally kind.

[edit] Trust game

The trust game extends the dictator game one step by having the reward that the dictator can (unilaterally) split between himself and a partner partially decided by an initial gift from that partner. The initial move is from the dictator's partner, who must decide how much of his or her initial endowment to trust with him (in the hopes of receiving some of it back). Normally, he is encouraged to give something to the dictator through a specification in the game's rules that her endowment will be increased by a factor from the researchers. The experiments rarely end in the subgame perfect Nash equilibrium of "no trust". In fact, a recent pair of studies of identical and fraternal twins in the USA and Sweden suggests that behavior in this game is heritable.^[8]

[edit] References

1. ^ ^{a b} Henrich, Joseph, Robert Boyd, Samuel Bowles, Colin Camerer, Ernst Fehr, and Herbert Gintis (2004) Foundations of Human Sociality: Economic Experiments and Ethnographic Evidence from Fifteen Small-Scale Societies. Oxford University Press.
2. ^ ^{a b c} Bardsley, Nicholas. (2005) "Altruism or artifact? A Note on Dictator Game Giving" CeDEx Discussion Paper No. 2005-10.
3. ^ For example, Bolton, Katok, Zwick 1998, "Dictator game giving: Rules of fairness versus acts of kindness" International Journal of Game Theory 27:2 (Article Abstract). This paper includes a review of dictator games going back to 1994 (Forsythe R, Horowitz JL, Savin NE, Sefton M, 1994 Fairness in simple bargaining experiments. in Games and Economic Behavior). For an overview see Camerer, Colin (2003) Behavioral Game Theory Princeton University Press, Princeton.
4. ^ Andreoni, J. and Miller, J. "Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism." Econometrica 70:2, 737-753.
5. ^ Fowler JH, Kam CD "Beyond the Self: Altruism, Social Identity, and Political Participation," Journal of Politics 69 (3): 811-825 (August 2007)
6. ^ Fowler JH. "Altruism and Turnout," Journal of Politics 68 (3): 674-683 (August 2006)
7. ^ Hoffman Elizabeth, McCabe Kevin, Shachat Keith and Smith Vernon (1994) "Preferences, Property Rights, and Anonymity in Bargaining Games" Games and Economic Behavior 7(3): 346-380 and Bolton, Gary E., Elena Katok, and Rami Zwick (1998) "Dictator game giving: Rules of fairness versus acts of kindness" [1] International Journal of Game Theory 27:269-299.
8. ^ Cesarini, David; Christopher T. Dawes, James H. Fowler, Magnus Johannesson, Paul Lichtenstein, Björn Wallace (11 March 2008). "Heritability of Cooperative Behavior in the Trust Game" (PDF). Proceedings of the National Academy of Sciences 105 (10): 3721-3726. doi:10.1073/pnas.0710069105. http://jhfowler.ucsd.edu/heritability_of_cooperative_behavior.pdf. 

[edit] Further reading

• Haley, K.; D. Fessler (2005). "Nobody’s watching? Subtle cues affect generosity in an anonymous economic game". Evolution and Human Behaviour 26: 245–256. doi:10.1016/j.evolhumbehav.2005.01.002.  Concludes that people tend to be more generous if there is a picture of a pair of eyes watching them.

• For a recent review of the dictator game in experiments see Angela A. Stanton: Evolving Economics: Synthesis

v • d • e Topics in game theory Definitions Normal-form game · Extensive-form game · Cooperative game · Information set · Preference Equilibrium concepts Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance · Pareto efficiency · Quantal response equilibrium · Self-confirming equilibrium Strategies Dominant strategies · Pure strategy · Mixed strategy · Tit for tat · Grim trigger · Collusion · Backward induction Classes of games Symmetric game · Perfect information · Dynamic game · Sequential game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Bargaining problem · Stochastic game · Nontransitive game · Global games Games Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Centipede game · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock-paper-scissors · Pirate game · Dictator game · Public goods game · Blotto games · War of attrition · El Farol Bar problem · Cake cutting · Cournot game · Deadlock · Diner's dilemma · Guess 2/3 of the average · Kuhn poker · Nash bargaining game · Screening game · Trust game · Princess and monster game Theorems Minimax theorem · Purification theorem · Folk theorem · Revelation principle · Arrow's impossibility theorem See also Tragedy of the commons · All-pay auction · List of games in game theory