Noncooperative Stochastic Games

Sobel, Milton

doi:10.1214/aoms/1177693059

Cited by 177 publications

(94 citation statements)

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“…In such games, there is an underlying set of states, and the game shifts between these states from stage to stage (Fudenberg and Tirole, 1991;Shapley, 1953;Sobel, 1971). At every stage, each player's payoff depends not only on the players' actions, but also on the state.…”

Section: Pure-strategy Nash Equilibria In Stochastic (Markov) Gamesmentioning

confidence: 99%

New complexity results about Nash equilibria

Conitzer

Sandholm

2008

Games and Economic Behavior

225

270

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We provide a single reduction that demonstrates that in normal-form games: (1) it is N P-complete to determine whether Nash equilibria with certain natural properties exist (these results are similar to those obtained by Gilboa and Zemel [Gilboa, I., Zemel, E., 1989. Nash and correlated equilibria: Some complexity considerations. Games Econ. Behav. 1, 80-93]), (2) more significantly, the problems of maximizing certain properties of a Nash equilibrium are inapproximable (unless P = N P), and (3) it is #P-hard to count the Nash equilibria. We also show that determining whether a pure-strategy Bayes-Nash equilibrium exists in a Bayesian game is N P-complete, and that determining whether a pure-strategy Nash equilibrium exists in a Markov (stochastic) game is PSPACE-hard even if the game is unobserved (and that this remains N P-hard if the game has finite length). All of our hardness results hold even if there are only two players and the game is symmetric.

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Section: Pure-strategy Nash Equilibria In Stochastic (Markov) Gamesmentioning

confidence: 99%

New complexity results about Nash equilibria

Conitzer

Sandholm

2008

Games and Economic Behavior

225

270

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“…See also Majumder and Groenevelt [61] for the analysis of deterministic time-dependent multiperiod games in reverse logistics supply chains. Stochastic games were developed by Shapley [84] and later by Heyman and Sobel [45], Kirman and Sobel [48], and Sobel [89]. The theory of stochastic games is also extensively covered in Filar and Vrieze [36].…”

Section: Cachon and Netessine: Game Theorymentioning

confidence: 99%

Game Theory in Supply Chain Analysis

Cachon¹,

Netessine²

2006

Models, Methods, and Applications for Innovative Decision Making

168

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Game theory has become an essential tool in the analysis of supply chains with multiple agents, often with conflicting objectives. This chapter surveys the applications of game theory to supply chain analysis and outlines game-theoretic concepts that have potential for future application. We discuss both noncooperative and cooperative game theory in static and dynamic settings. Careful attention is given to techniques for demonstrating the existence and uniqueness of equilibrium in noncooperative games. A newsvendor game is employed throughout to demonstrate the application of various tools.

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“…See also Majumder and Groenevelt (2001b) for the analysis of deterministic time-dependent multi-period games in reverse logistics supply chains. Stochastic games were developed by Shapley (1953a) and later by Sobel (1971), Kirman and Sobel (1974) and Heyman and Sobel (1984). The theory of stochastic games is also extensively covered in Filar and Vrieze (1996).…”

Section: Simultaneous Moves: Repeated and Stochastic Gamesmentioning

confidence: 99%

Game Theory in Supply Chain Analysis

Cachon

Netessine

2004

International Series in Operations Research &Amp; Management Science

306

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Game theory has become an essential tool in the analysis of supply chains with multiple agents, often with conflicting objectives. This chapter surveys the applications of game theory to supply chain analysis and outlines game-theoretic concepts that have potential for future application. We discuss both non-cooperative and cooperative game theory in static and dynamic settings. Careful attention is given to techniques for demonstrating the existence and uniqueness of equilibrium in non-cooperative games. A newsvendor game is employed throughout to demonstrate the application of various tools. 1

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Noncooperative Stochastic Games

Cited by 177 publications

References 0 publications

New complexity results about Nash equilibria

New complexity results about Nash equilibria

Game Theory in Supply Chain Analysis

Game Theory in Supply Chain Analysis

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