Dictator game

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, although this conclusion is controversial.

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 himself. The responder's role is entirely passive (he 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 players' 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 name persists in the game theory literature because of the result's usefulness to game theory at large.

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 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. These results appear robust, Henrich, et al. discovered in a wide cross cultural study that proposers do allocate a non-zero share of the endowment to the responder.

If these experiments appropriately reflect individuals' preferences outside of the laboratory, these results appears to demonstrate that either:
 * 1) Proposers fail to maximize their own expected utility, or
 * 2) Proposer's utility functions include benefits received by others.

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.

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. In these cases individuals consistently give less (close to zero). Bardsley suggests two interpretations for these results. First, it may be that the range of options cues experimental subjects to use different reasoning patterns. "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." 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, and as a result giving less appears equally kind.

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 her initial endowment to trust with him (in the hopes of receiving some of it back). Normally, she 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."