Tenable Strategy Blocks and Settled Equilibria
研究了有限正规型博弈中两种可维持策略块概念(粗与细),并识别出稳定均衡(最小可维持块中的纳什均衡),通过例子展示其性质与力量,与持久均衡相比更具选择性。
When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set-valued concepts, coarsely and finely tenable blocks, that formalize this notion for finite normal-form games. We then identify settled equilibria, which are Nash equilibria with support in minimal tenable blocks. For a generic class of normal-form games, our coarse and fine concepts are equivalent, and yet they differ from standard solution concepts on open sets of games. We demonstrate the nature and power of the solutions by way of examples. Settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games. With fine tenability, we obtain invariance under the insertion of a subgame with a unique totally mixed payoff-equivalent equilibrium, a property that other related concepts have not satisfied.