Hiring and firing -- a signaling game

TL;DR

This paper models a signaling game between an employer and employee with private information, using stochastic processes and optimal stopping to analyze strategic communication and firing decisions.

Contribution

It introduces a novel equilibrium analysis combining filtering and stopping theory in a signaling game with private information and dynamic decision-making.

Findings

Employees provide randomized salary claims as signals.

Employers adopt threshold strategies based on conditional probabilities.

The model's methodology extends to various scenarios with additional complexities.

Abstract

We study a signaling game between an employer and a potential employee, where the employee has private information regarding their production capacity. At the initial stage, the employee communicates a salary claim, after which the true production capacity is gradually revealed to the employer as the unknown drift of a Brownian motion representing the revenues generated by the employee. Subsequently, the employer has the possibility to choose a time to fire the employee in case the estimated production capacity falls short of the salary. In this set-up, we use filtering and optimal stopping theory to derive an equilibrium in which the employee provides a randomized salary claim and the employer uses a threshold strategy in terms of the conditional probability for the high production capacity. The analysis is robust in the sense that various extensions of the basic model can be solved using the same methodology, including cases with positive firing costs, incomplete information about one's own type, as well as an additional interview phase.