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The ultimatum game is a game in economic experiments. The first player (the proposer) receives a sum of money and proposes how to divide the sum between himself and another player. The second player (the responder) chooses to either accept or reject this proposal. If the second player accepts, the money is split according to the proposal. If the second player rejects, neither player receives any money. The game is typically played only once so that reciprocation is not an issue. == Equilibrium analysis == For illustration, we will suppose there is a smallest division of the good available (say 1 cent). Suppose that the total amount of money available is ''x''. The first player chooses some amount ''p'' he will keep for himself in the interval (), the second player will then receive ''x''-''p''. The second player chooses some function ''f'': (''x'' ) → (i.e. the second chooses which divisions to accept and which to reject). We will represent the strategy profile as (''p'', ''f''), where ''p'' is the proposal and ''f'' is the function. If ''f''(''p'') = "accept" the first receives ''p'' and the second ''x''−''p'', otherwise both get zero. (''p'', ''f''(''p'')) is a Nash equilibrium of the ultimatum game if ''f''(''p'') = "accept" and there is no ''y'' > ''p'' such that ''f''(''y'') = "accept" (i.e. player 2 would reject all proposals in which player 1 receives more than ''p''). The first player would not want to unilaterally increase his/her demand since the second would reject any higher demand. The second would not want to reject the demand, since he/she would then get nothing. There is one other Nash equilibrium where ''p'' = ''x'' and ''f''(''y'') = "reject" for all ''y''>0 (i.e. the second rejects all demands that gives the first any amount at all). Here both players get nothing, but neither could get more by unilaterally changing his/her strategy. However, only one of these Nash equilibria satisfies a more restrictive equilibrium concept, subgame perfection. Suppose that the first demands a large amount that gives the second some (small) amount of money. By rejecting the demand, the second is choosing nothing rather than something. So, it would be better for the second to choose to accept any demand that gives him/her any amount whatsoever. If the first knows this, he/she will give the second the smallest (non-zero) amount possible.〔Technically, making a zero offer to the responder and accepting this offer is also a Nash Equilibrium, as the responder's threat to reject the offer is no longer credible, since he/she now gains nothing (materially) by refusing the zero amount offered. Normally, when a player is indifferent between various strategies, the principle in Game Theory is that the strategy with an outcome which is Pareto optimally better for the other players is chosen (as a sort of tie-breaker to create a unique NE). However, it is generally assumed that this principle should not apply to ultimatum game players offered nothing; they are instead assumed to reject the offer although accepting it would be an equally subgame perfect NE. For instance, the University of Wisconsin summary: (Testing Subgame Perfection Apart From Fairness in Ultimatum Games ) from 2002 admits the possibility that the proposer may offer nothing but qualifies the subgame perfect NE with the words (almost nothing) throughout the Introduction.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ultimatum game」の詳細全文を読む スポンサード リンク
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