Stochastic Multi-player Competitive Games in Discrete Time

TL;DR

This paper introduces a new class of multi-player stochastic games with affine payoff redistribution, extending classic stopping games, and provides conditions for equilibrium existence and solution methods for multi-period cases.

Contribution

It proposes a novel class of multi-player stochastic games with affine payoff redistribution and extends existing results to multi-period stochastic affine games.

Findings

Existence conditions for optimal equilibria and game values.

Backward induction method for solving multi-period affine games.

Extension of classic two-player stopping game results.

Abstract

A new class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is proposed and examined. Our games cover as a very special case the classic two-person stochastic stopping games introduced by Dynkin (1969). We first extend to the case of a single-period deterministic affine game the results from Guo and Rutkowski (2012,2014) where a particular subclass of competitive stopping games was studied. We identify conditions under which optimal equilibria and value for a multi-player competitive game with affine redistribution of payoffs exist. We also examine stochastic multi-period affine games and we show that, under mild assumptions, they can be solved by the backward induction.