A formula for the value of a stochastic game

TL;DR

This paper presents a new, tractable formula for determining the value of competitive stochastic games, building on foundational work by Shapley and Mertens-Neyman.

Contribution

It introduces a novel formula that simplifies the calculation of the value in stochastic games, advancing theoretical understanding.

Findings

Derived a closed-form formula for stochastic game value

Simplifies computation of game values

Enhances theoretical framework for stochastic games

Abstract

In 1953, Lloyd Shapley defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that competitive stochastic games have a discounted value. In 1982, Jean-Fran\c{c}ois Mertens and Abraham Neyman proved that competitive stochastic games admit a robust solution concept, the value, which is equal to the limit of the discounted values as the discount rate goes to 0. Both contributions were published in PNAS. In the present paper, we provide a tractable formula for the value of competitive stochastic games.