![]() So, the first two Nash equilibria above are 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. The theory relies on the assumption that players are rational and utility maximising. A perfect-subgame equilibrium occurs when there are Nash Equilibria in every subgame, that players have no incentive to deviate from. The above 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 last Nash equilibrium satisfies a more restrictive equilibrium concept, subgame perfection. The proposer makes an unfair offer the responder would accept any offer.The proposer makes an unfair offer the responder would only accept an unfair offer.The proposer makes a fair offer the responder would only accept a fair offer.So, there are three Nash equilibria for this game: ![]() Meanwhile, it benefits the proposer to make an offer that the responder will accept furthermore, if the responder would accept any offer, then it benefits the proposer to switch from a fair to an unfair offer. It always benefits the responder to accept the offer, as receiving something is better than receiving nothing. For each of these two splits, the responder can choose to accept or reject, which means that there are four strategies available to the responder: always accept, always reject, accept only a fair split, or accept only an unfair split.Ī Nash equilibrium is a pair of strategies (one for the proposer and one for the responder), where neither party can improve their reward by changing strategy. There are two strategies available to the proposer: propose a fair split, or propose an unfair split. The argument given in this section can be extended to the more general case where the proposer can choose from many different splits. 2 Multi-valued or continuous strategiesįor ease of exposition, the simple example illustrated above can be considered, where the proposer has two options: a fair split, or an unfair split.
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