Subgame-Perfect Equilibria in Stochastic Timing Games

TL;DR

This paper develops a framework for subgame-perfect equilibria in stochastic timing games, especially in continuous time, providing existence results and applications to preemption games in real options.

Contribution

It introduces a new notion of subgames and equilibria for stochastic timing games, filling a gap in continuous-time game theory and enabling analysis of mixed strategies.

Findings

Established a consistent notion of subgame-perfect equilibrium for continuous-time timing games.

Proved existence of equilibria in preemption games within this framework.

Applied the theory to explicit examples demonstrating its usefulness.

Abstract

We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies -- in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications.