# Playing with ghosts in a Dynkin game

## TL;DR

This paper analyzes a class of preemption-type Dynkin games with uncertainty about competitors, providing explicit Nash equilibrium solutions in terms of one-player game analysis, relevant for modeling strategic investment decisions.

## Contribution

It introduces a framework for optimal stopping games with uncertainty about competitors and explicitly characterizes Nash equilibria in randomized stopping times.

## Key findings

- Existence of Nash equilibrium in randomized stopping times.
- Explicit characterization of equilibrium via one-player game.
- Applicability to real options and strategic investment modeling.

## Abstract

We study a class of optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal their interest in a certain business opportunity. We show that there exists a Nash equilibrium in randomized stopping times which is described explicitly in terms of the corresponding one-player game.