11. Extensive Games and the Problem of Information

Kuhn, Harold W.

doi:10.1515/9781400881970-012

Cited by 551 publications

(417 citation statements)

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“…Their classic book "Theory of Games and Economic Behavior", von Neumann and Morgenstern (1944), summarizes the basic concepts existing at that time. GT has since enjoyed an explosion of developments, including the concept of equilibrium by Nash (1950), games with imperfect information by Kuhn (1953), cooperative games by Aumann (1959) and Shubik (1962) and auctions by Vickrey (1961), to name just a few. Citing Shubik (2002), "In the 50s ... game theory was looked upon as a curiosum not to be taken seriously by any behavioral scientist.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Game Theory in Supply Chain Analysis

Cachon

Netessine

2004

International Series in Operations Research &Amp; Management Science

306

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“…Following Kuhn 1953 andShapley 1953, consider a dynamic stochastic game G with n players indexed by i ∈ {1, . .…”

Section: Finite State Markovian Gamesmentioning

confidence: 99%

“…State recursion can be viewed as a generalization of the method of backward induction that Kuhn 1953 andSelten 1965 proposed as a method to find subgame perfect equilibria of finite extensive form games. However, the backward induction that Kuhn and Selten analyzed is performed on the game tree of the extensive form representation of the game.…”

Section: Introductionmentioning

confidence: 99%

Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games

Iskhakov¹,

Rust²,

Schjerning³

2015

Review of Economic Studies

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Abstract:We define a class of dynamic Markovian games, directional dynamic games (DDG), where directionality is represented by a strategy-independent partial order on the state space. We show that many games are DDGs, yet none of the existing algorithms are guaranteed to find any Markov perfect equilibrium (MPE) of these games, much less all of them. We propose a fast and robust generalization of backward induction we call state recursion that operates on a decomposition of the overall DDG into a finite number of more tractable stage games, which can be solved recursively. We provide conditions under which state recursion finds at least one MPE of the overall DDG in a finite number of steps. We introduce a recursive lexicographic search (RLS) algorithm that systematically and efficiently uses state recursion to find all MPE of the overall game in a finite number of steps. We apply RLS to find all MPE of a dynamic model of Bertrand price competition with cost reducing investments which we show is a DDG. RLS rapidly finds and enumerates each one of the hundreds of millions of MPE of this game.

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“…k of the same player i, if one node y, y ∈u i . k , comes after a choice c at u i. j , then every node x in u i. k comes after the same choice c. By Kuhn's theorem [11], in the presence of perfect recall, one can restrict the analysis to behavioral strategies.…”

Section: Definitionmentioning

confidence: 99%

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Sánchez¹,

García²

1998

Annals of Operations Research

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Credible equilibria were defined in Ferreira et al. [6] to handle situations of preferences changing along time in a model given by an extensive form game. This paper extends the definition to the case of infinite games and, more important, to games with non-perfect recall. These games are of great interest in possible applications of the model, but the original definition was not applicable to them. The difficulties of this extension are solved by using some ideas in the literature of abstract systems and by proposing new ones that may prove useful in more general settings.

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11. Extensive Games and the Problem of Information

Cited by 551 publications

References 0 publications

Game Theory in Supply Chain Analysis

Game Theory in Supply Chain Analysis

Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games

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