Multi-Principal Competition for an Exclusive Agent: characterization and approximation of Nash Equilibria
arXiv:2609.04426
Abstract
This paper introduces and studies a Principal-Agent competition model where two risk-neutral Principals compete to hire a single Agent. In this framework, the Agent chooses to work exclusively for one Principal, making the Agent's reservation utility endogenous as it is directly tied to the competing offers. We characterize the Nash equilibria of the resulting game by linking them to the individual Principal-Agent contracting problems and analyzing the Agent's selection bias. Furthermore, we introduce a numerical algorithm based on the bisection method to approximate the Nash equilibria by locating the sign changes of the Principals' value functions. The procedure is illustrated through several examples involving exponential, logarithmic, and constant relative risk aversion (CRRA) utility functions within the polynomial framework of Renner and Schmedders (2015).
3 figures