序贯竞赛中失败情形下的最优策略
Optimal Strategies in a Sequential Contest with Failures
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中文总结 AI 辅助
本文研究序贯竞赛中玩家可能失败的情形，提出跟随者与领导者的最优策略，并分析能力与失败成本异质性对博弈结果的影响。
中文摘要 AI 辅助
我们研究了一个Stackelberg模型，其中两名玩家参与序贯竞赛，成功投入最多努力的玩家获胜。我们的模型考虑了每位玩家未能投入其选定努力水平的概率，这由随努力量增加而增大的失败函数刻画。每位玩家有各自的失败成本，以及最大努力水平（体现玩家能力差异）。我们证明了三个关键结果。首先，我们给出了玩家1（跟随者）的最优策略，以在观察到玩家2（领导者）投入的努力后最大化其效用。其次，我们刻画了玩家2在预期玩家1最优反应下最大化期望效用的最优策略。最后，我们分析了双方均采用最优策略时每位玩家的期望效用，并就玩家能力异质性和失败成本如何影响博弈结果提供了关键见解。
英文摘要
We study a Stackelberg model where two players compete in a sequential contest, and the player that successfully invests the most effort wins. Our formulation considers a probability that each player fails to invest their chosen level of effort, as captured by a failure function that increases with the amount of effort. The players each have their own cost of failure, as well as a maximum level of effort (capturing different abilities of the players). We prove three key results. First, we provide the optimal strategy for Player 1 (the follower), to maximize their utility given an observed effort exerted by Player 2 (the leader). Next, we characterize the optimal strategy to maximize the expected utility of Player 2, anticipating the optimal response by Player 1. Finally, we analyze the expected utilities of each player when both play their optimal strategy, and provide key insights into how heterogeneous player abilities and failure costs affect the outcomes of the game.
发表机构
- Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。
