Hiring and firing -- a signaling game

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.

Figures (2)

• Figure 1: The value function $V(\pi)$ of the employer in the case when $C=c_1$ is chosen. The parameter values chosen for this example figure are $c_1=1.5$, $\mu_0=1.4$, $\mu_1=1.7$, $r=0.05$ and $\sigma=1$. The value function attains positive values only after the boundary level $b \approx 0.167$, and it approaches its maximum value $(\mu_1-c_1)/r$ for $\pi$ close to 1.
• Figure 2: The value function $U(\pi)$ for the weak type employee when the high salary $C = c_1$ is chosen. The parameter values of $c_1$, $\mu_0$, $\mu_1$, $r$ and $\sigma$ are the same as in Figure \ref{['fig:V_plot']}, and $c_0=1.2$. Here $\hat{p}$ is the unique value so that $U(\hat{p})=c_0/r$.

Theorems & Definitions (11)

• Remark \oldthetheorem
• Remark \oldthetheorem
• Definition \oldthetheorem
• Remark \oldthetheorem
• Remark \oldthetheorem
• Lemma \oldthetheorem
• proof
• Theorem \oldthetheorem
• proof
• Remark \oldthetheorem