The simplest version of the ultimatum game has two possible strategies for the proposer, Fair and Unfair. So, the second set of Nash equilibria above is not subgame perfect: the responder can choose a better strategy for one of the subgames. In both subgames, it benefits the responder to accept the offer. A perfect-subgame equilibrium occurs when there are Nash Equilibria in every subgame, that players have no incentive to deviate from. The game can be viewed as having two subgames: the subgame where the proposer makes a fair offer, and the subgame where the proposer makes an unfair offer. However, only the first set of Nash equilibria satisfies a more restrictive equilibrium concept, subgame perfection. The responder rejects unfair offers often enough to make fair offers at least as profitable as unfair offers, and always accepts fair offers. The proposer always makes a fair offer.(The proposer never gives a fair offer so the responder can accept fair offers with any frequency without affecting the average reward.) ![]() The proposer always makes an unfair offer, and the responder always accepts an unfair offer.Thus, there are two sets of Nash equilibria for this game: Any change in strategy by the responder will result in the same reward or less. Any change in strategy by the proposer will lower their reward. Although it always benefits the responder to accept even unfair offers, the responder can adopt a strategy that rejects unfair splits often enough to induce the proposer to always make a fair offer. If the proposer always makes an unfair offer, the responder will do best by always accepting the offer, and the proposer will maximize their reward. The argument given in this section can be extended to the more general case where the proposer can choose from many different splits.Ī Nash equilibrium is a set of strategies (one for the proposer and one for the responder in this case), where no individual party can improve their reward by changing strategy. Both players know in advance the consequences of the responder accepting or rejecting the offer.įor ease of exposition, the simple example illustrated above can be considered, where the proposer has two options: a fair split, or an unfair split. If the responder accepts, the money is split per the proposal if the responder rejects, both players receive nothing. Once the proposer communicates his decision, the responder may accept it or reject it. ![]() The proposer is tasked with splitting it with another player, the responder (who knows what the total sum is). One player, the proposer, is endowed with a sum of money. An early description is by Nobel laureate John Harsanyi in 1961. The ultimatum game is a game that has become a popular instrument of economic experiments. Player 1 can offer a fair (F) or unfair (U) proposal player 2 can accept (A) or reject (R). ( Learn how and when to remove this template message)Įxtensive form representation of a two proposal ultimatum game. ( January 2021) ( Learn how and when to remove this template message) There might be a discussion about this on the talk page. This article may be confusing or unclear to readers.
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