Dynkin ghost games with asymmetry and consolation

TL;DR

This paper analyzes a two-player stopping game with asymmetrical payoffs and consolation, providing a verification theorem to construct equilibria in complex uncertain competition scenarios.

Contribution

It introduces a novel framework for preemption games incorporating payoff asymmetry and consolation, with a general method to establish equilibria.

Findings

Verification theorem for equilibrium construction

Impact of asymmetry on stopping strategies

Role of consolation in game outcomes

Abstract

We study a stopping game of preemption type between two players who both act under uncertain competition. In this framework we introduce, and study the effect of, (i) asymmetry of payoffs, allowing e.g. for different investment costs, and (ii) consolation, i.e. partial compensation to the forestalled stopper. In general, this setting does not offer an explicit equilibrium. Instead, we provide a general verification theorem, which we then use to explore various situations in which a solution can be constructed so that an equilibrium is obtained.