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Stochastic games

Eilon Solan¹, Nicolas Vieille²

¹Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 6997800, Israel; eilons@post.tau.ac.il vieille@hec.fr.

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

|November 12, 2015

Summary

Lloyd Shapley introduced stochastic games in 1953, establishing the first general dynamic game model. His work proved the existence of a stationary equilibrium, a foundational concept in game theory.

Area of Science:

Game Theory
Mathematical Economics
Decision Sciences

Background:

Lloyd Shapley's 1953 PNAS paper introduced "stochastic games."
This marked the first general dynamic model for game theory.
The paper established foundational concepts in strategic interaction.

Purpose of the Study:

To summarize the historical context of Shapley's stochastic games.
To analyze the profound impact of this seminal contribution.
To highlight the significance of stationary equilibrium in dynamic games.

Main Methods:

Historical analysis of Shapley's 1953 paper.
Review of subsequent research and citations.
Conceptual analysis of dynamic game models.

Main Results:

Shapley defined the model of stochastic games.
He proved the existence of a stationary equilibrium.
The paper laid the groundwork for modern dynamic game theory.

Conclusions:

Shapley's stochastic games are a cornerstone of game theory.
The concept of stationary equilibrium remains critical.
This work continues to influence research in economics and beyond.

Keywords:

game theory stochastic games

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