Existence of Undominated Subgame Perfect Equilibrium in Extensive Form Games.

摘要

There are games for which all subgame perfect equilibria are such that some (or all) players use weakly dominated strategies. Surely this is undesirable as it diminishes the credibility of equilibria. It is implausible to expect a player to play a weakly dominated strategy just because it is an 'equilibrium strategy'. We focus on the class of finite extensive form games with complete and perfect information and show that in this class of games there exists an undominated subgame perfect equilibrium; a subgame perfect equilibrium in which no player uses a weakly dominated strategy. The results also provide insight as to why one should restrict the class of mechanisms to finite mechanisms where relevant.