多提议者—多响应者最后通牒博弈中的公平性
Fairness in Multi-Proposer-Multi-Responder Ultimatum Game
AI总结：
本文提出多提议者—多响应者最后通牒博弈，刻画群体竞争下的子博弈完美纳什均衡，并据渐近参与者数量给出响应者公平份额阈值31.8%或36.8%。
摘要：
最后通牒博弈通常以两名参与者的情境来表述。然而，现实生活场景往往涉及众多个体之间的共同体互动。为解决这一问题，我们引入最后通牒博弈的扩展版本，称为多提议者—多响应者最后通牒博弈。在该模型中，多名响应者与提议者在一次单阶段博弈中同时互动，从而在提议者内部和响应者内部都引入竞争。我们推导了所有情形下的子博弈完美纳什均衡，并探讨这些非平凡数值如何能够解释在一对一最后通牒博弈情境中通过实验观察到的提议与拒绝行为。此外，通过考虑参与者数量的渐近情形，我们提出了“公平”阈值的两种可能估计：响应者获得蛋糕（份额）的31.8%或36.8%。
英文摘要：
The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum Game. In this model, multiple responders and proposers simultaneously interact in a one-shot game, introducing competition both within proposers and within responders. We derive subgame-perfect Nash equilibria for all scenarios and explore how these non-trivial values might provide insight into proposal and rejection behavior experimentally observed in the context of one vs. one Ultimatum Game scenarios. Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a "fair" threshold: either 31.8% or 36.8% of the pie (share) for the responder.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
