Exit game with private information

TL;DR

This paper analyzes a stochastic game of exit under private information, deriving explicit equilibrium strategies based on the state and belief processes, and proving their uniqueness within symmetric Bayesian equilibria.

Contribution

It introduces a novel equilibrium construction for a class of stochastic exit games with private information, explicitly characterizing strategies and establishing uniqueness.

Findings

Explicit equilibrium strategies involving state and belief variables.

Equilibrium strategies are derived from an auxiliary optimal stopping problem.

Uniqueness of the equilibrium within symmetric Bayesian strategies.

Abstract

The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about their competitor's exit value. We construct an equilibrium for a large class of payoff flows driven by a general one-dimensional diffusion. In the equilibrium, the players employ sophisticated exit strategies involving both the state variable and the posterior belief process. These strategies are specified explicitly in terms of the problem data and a solution to an auxiliary optimal stopping problem. The equilibrium we obtain is further shown to be unique within a wide subclass of symmetric Bayesian equilibria.