多委托人针对专属代理人的竞争：纳什均衡的刻画与近似
Multi-Principal Competition for an Exclusive Agent: characterization and approximation of Nash Equilibria
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中文总结 AI 辅助
本文研究两名风险中性委托人竞争雇佣专属代理人的委托-代理博弈，刻画其纳什均衡并提出基于二分法的数值算法近似，结合多类效用函数实例验证。
中文摘要 AI 辅助
本文引入并研究了一个委托-代理竞争模型，其中两名风险中性的委托人竞争雇佣一名代理人。在该框架下，代理人选择只为一名委托人工作，因此代理人的保留效用是内生的，因为它直接与竞争的报价挂钩。我们通过将该博弈的纳什均衡与单个委托-代理缔约问题关联并分析代理人的选择偏差，来刻画纳什均衡。此外，我们提出了一种基于二分法的数值算法，通过定位委托人价值函数的符号变化来近似纳什均衡。该过程通过多个实例进行说明，这些实例涉及指数、对数和常数相对风险厌恶（CRRA）效用函数，属于Renner和Schmedders（2015）的多项式框架。
英文摘要
This paper introduces and studies a Principal-Agent competition model in which two risk-neutral Principals compete to hire a single Agent. The Agent chooses to work exclusively for one Principal, making the Agent's reservation utility endogenous, as it is determined by the competing offers. We characterize the Nash equilibria of the resulting game by relating them to the individual Principal-Agent contracting problems and analyzing the Agent's selection bias. We further introduce two numerical algorithms to approximate Nash equilibria by locating sign changes of the value functions of the Principals' individual problems. The first is a Newton-type method that exploits differentiability of the value functions, while the second is a bisection method that does not require differentiability. The proposed procedures are illustrated through several examples involving exponential, logarithmic, and constant relative risk aversion (CRRA) utility functions within the polynomial framework of Renner and Schmedders (2015). We also provide technical results regarding the regularity of the value function of a classical Principal-Agent problem, including differentiability under suitable conditions.
发表机构
- Universidad Técnica Federico Santa María（弗雷德里克·萨马拉技术大学）
机构由 AI 辅助整理，请以论文原文为准。
