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Stochastic games have a value.

J F Mertens¹, A Neyman

¹Center for Operations Research and Econometrics and Department of Mathematics, Université Catholique de Louvain, Louvain-la Neuve, Belgium.

Proceedings of the National Academy of Sciences of the United States of America

|March 1, 1982

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This study demonstrates that undiscounted nonterminating stochastic games with finite states and actions possess a defined value. This finding is crucial for understanding game theory and decision-making in complex systems.

Area of Science:

Game Theory
Decision Theory
Mathematical Economics

Background:

Stochastic games are mathematical models used to analyze sequential decision-making under uncertainty.
The concept of a 'value' in game theory refers to the expected payoff a player can guarantee.

Purpose of the Study:

To establish the existence of a value for a specific class of stochastic games.
To contribute to the theoretical foundations of game theory.

Main Methods:

Analysis of undiscounted nonterminating stochastic games.
Focus on games with finite state and action spaces.

Main Results:

The core finding is the proof that such games always have a value.

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This value represents the optimal outcome achievable by the players.

Conclusions:

The existence of a value is a fundamental property of these games.
This result has implications for equilibrium analysis and strategic planning.