Acceptable Strategy Profiles in Stochastic Games

TL;DR

This paper introduces the concept of acceptable strategy profiles in multiplayer stochastic games, ensuring each player's payoff exceeds a specified threshold at all states when the discount factor is near 1.

Contribution

It proposes a new solution concept for stochastic games, providing simple strategies that guarantee high payoffs for all players across states.

Findings

Defined the $w$-acceptable strategy profile concept.

Established conditions for strategies to be $w$-acceptable.

Showed existence of simple strategies for high payoff vectors.

Abstract

This paper presents a new solution concept for multiplayer stochastic games, namely, acceptable strategy profiles. For each player $i$ and state $s$ in a stochastic game, let $w_i(s)$ be a real number. A strategy profile is \emph{$w$-acceptable}, where $w=(w_i(s))$, if the discounted payoff to each player $i$ at every initial state $s$ is at least $w_i(s)$, provided the discount factor of the players is sufficiently close to 1. Our goal is to provide simple strategy profiles that are $w$-acceptable for payoff vectors $w$ in which all coordinates are high.