Unilaterally Competitive Multi-Player Stopping Games

TL;DR

This paper introduces a multi-player Dynkin stopping game with a novel explicit solution for Nash and optimal equilibria, exploring its multi-period extensions and applications in economics and finance, especially in game option pricing.

Contribution

It provides the first explicit construction of the unique value and equilibria in multi-player stopping games, extending to multiple periods and applications in financial modeling.

Findings

The game is weakly unilaterally competitive in the single period case.

Explicit solutions for Nash and optimal equilibria are derived.

Applications include pricing of multi-person financial game options.

Abstract

A multi-player competitive Dynkin stopping game is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single period case is shown to be "weakly unilaterally competitive". We present an explicit construction of the unique value at which Nash and optimal equilibria are attained. Multiple period generalisations are explored. The game has interpretations in economic and financial contexts, for example, as a consumption model with bounded resources. It also serves as a starting point to the construction of multi-person financial game options. In particular, the concept of optimal equilibria becomes pivotal in the pricing of the game options via super-replication.