Consider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM's choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM's choice correspondence fails to satisfy WARP. First, Sen's axiom alpha is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen's axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games.

中文翻译：

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反向归纳和子博弈完美的显示偏好含义

考虑一个决策者 (DM)，他必须从一组相互排斥的备选方案中选择一个备选方案，但必须按顺序做出这个决定。如果 DM 对备选方案子集的选择对应满足显示偏好弱公理 (WARP)，则子博弈完美纳什均衡 (SPNE) 和反向归纳 (BI) 策略重合。我们研究了当 DM 的选择对应不能满足 WARP 时 SPNE 和 BI 策略之间的关系。首先，Sen 公理 alpha 对 SPNE 策略集是 BI 策略集的子集是必要和充分的；此外，对于将 BI 策略集作为 SPNE 策略集的子集，Sen 公理 β 的温和加强是必要且充分的。这些结果扩展到多人游戏。