p-Dominance and Belief Potential
提出信念潜力和p-占优两个新概念,证明当纳什均衡的p-占优低于信念潜力时,该均衡被唯一选择。该标准适用于多行动博弈和无占优策略博弈,有助于理解均衡集如何随共同知识量变化。
This paper elucidates the logic behind recent papers which show that a unique equilibrium is selected in the presence of higher order uncertainty, i.e., when players lack common knowledge.We introduce two new concepts: belief potential of the information system and p-dominance of Nash-equilibria of the game, and show that a Nash-equilibrium is uniquely selected whenever its p-dominance is below the belief potential.This criterion applies to many-action games, not merely 2 x 2 games.It also applies to games without dominant strategies, where the set of equilibria is shown to be smaller and simpler than might be initially conjectured.Finally, the new concepts help understand the circumstances under which the set of equilibria varies with the amount of common knowledge among players.