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Everything about Trust Game totally explained

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 isn't 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. 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. 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.

Challenges

Some authors have suggested that giving in the dictator game doesn't 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 most individuals far from showing altruism actually take money. 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." 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.

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's 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."

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