Equilibria in Quitting Games - Basics

TL;DR

This paper analyzes the structure of quitting games, a simple class of stochastic games, focusing on equilibria and their relation to one-step game properties, aiming to facilitate equilibrium detection algorithms.

Contribution

It provides a detailed analysis of equilibria in quitting games and their connection to one-step game properties, laying groundwork for equilibrium detection algorithms.

Findings

Properties of expected payoffs in one-step games

Relations between equilibria in one-step and quitting games

Foundations for algorithms to detect quitting game equilibria

Abstract

Quitting games are one of the simplest stochastic games in which at any stage each player has only two possible actions, continue and quit. The game ends as soon as at least one player chooses to quit. The players then receive a payoff, which depends on the set of players that did choose to quit. If the game never ends, the payoff to each player is zero. For analysis of quitting games the so called one-step games are used. Important properties of the expected payoff and of equilibria in one-step games are stated. Furthermore some relations between equilibria in one-step games and equilibria in quitting games are considered. This analysis of the structure of quitting games and the related one-step games should provide a basis for an implementation of an algorithm that detect equilibria in Quitting Games.