Computing a quasi-perfect equilibrium of a two-player game

Miltersen, Peter Bro; Sørensen, Troels Bjerre

doi:10.1007/s00199-009-0440-6

Cited by 27 publications

(29 citation statements)

References 16 publications

(23 reference statements)

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“…The subgame-perfect equilibrium forces the strategy profile to be a Nash equilibrium in each sub-game (i.e., in each sub-tree rooted in some node h) of the original game. Unfortunately, sub-games are not particularly useful in imperfectinformation EFGs; hence, here the refinements include strategic-from perfect equilibrium (Selten, 1975), sequential equilibrium (Kreps & Wilson, 1982), or quasi-perfect equilibrium (van Damme, 1984;Miltersen & Sørensen, 2010). The first refinement avoids using weakly dominated strategies in equilibrium strategies for two-player games (van Damme, 1991, p. 29) and it is also known as the undominated equilibrium.…”

Section: Nash Equilibrium In Extensive-form Gamesmentioning

confidence: 99%

An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information

Bošanský¹,

Kiekintveld²,

Lisý³

et al. 2014

jair

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Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the compact sequence-form representation of extensive-form games and (2) the algorithmic framework of double-oracle methods. The main idea of our algorithm is to restrict the game by allowing the players to play only selected sequences of available actions. After solving the restricted game, new sequences are added by finding best responses to the current solution using fast algorithms. We experimentally evaluate our algorithm on a set of games inspired by patrolling scenarios, board, and card games. The results show significant runtime improvements in games admitting an equilibrium with small support, and substantial improvement in memory use even on games with large support. The improvement in memory use is particularly important because it allows our algorithm to solve much larger game instances than existing linear programming methods. Our main contributions include (1) a generic sequence-form double-oracle algorithm for solving zero-sum extensive-form games; (2) fast methods for maintaining a valid restricted game model when adding new sequences; (3) a search algorithm and pruning methods for computing best-response sequences; (4) theoretical guarantees about the convergence of the algorithm to a Nash equilibrium; (5) experimental analysis of our algorithm on several games, including an approximate version of the algorithm.

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Section: Nash Equilibrium In Extensive-form Gamesmentioning

confidence: 99%

An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information

Bošanský¹,

Kiekintveld²,

Lisý³

et al. 2014

jair

View full text Add to dashboard Cite

show abstract

“…Subsequently, we define a class of perturbation schemes for the sequence form such that any limit point of a sequence of Stackelberg equilibria in perturbed games with vanishing perturbation is a quasi-perfect Stackelberg equilibrium. This class of perturbation schemes strictly includes those used to find a quasi-perfect equilibrium by [40]. Then, we extend the algorithm by [16] to the case of quasi-perfect Stackelberg equilibrium computation.…”

Section: Trembling-hand Perfection In Stackelberg Gamesmentioning

confidence: 99%

Leadership Games: Multiple Followers, Multiple Leaders, and Perfection

Marchesi

2021

Special Topics in Information Technology

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“…Watanabe and Yamato [24] used the same concept to study a choice of auction in seller cheating. Miltersen and Sørensen [25] proposed a computational method to find quasiperfect Nash equilibria for two-player games. While the perfectness verification problem is known to be easy with two players [26], to our knowledge, no results are reported on the perfect refinement of Nash equilibria for polymatrix games.…”

Section: Motivation Decision Makers Confronted To Multiplementioning

confidence: 99%

On Perfect Nash Equilibria of Polymatrix Games

Belhaiza

2014

Game Theory

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When confronted with multiple Nash equilibria, decision makers have to refine their choices. Among all known Nash equilibrium refinements, theperfectnessconcept is probably the most famous one. It is known that weakly dominated strategies of two-player games cannot be part of a perfect equilibrium. In general, thisundominanceproperty however does not extend ton-player games (E. E. C. van Damme, 1983). In this paper we show that polymatrix games, which form a particular class ofn-player games, verify the undominance property. Consequently, we prove that every perfect equilibrium of a polymatrix game is undominated and that every undominated equilibrium of a polymatrix game is perfect. This result is used to set a new characterization of perfect Nash equilibria for polymatrix games. We also prove that the set of perfect Nash equilibria of a polymatrix game is a finite union of convex polytopes. In addition, we introduce a linear programming formulation to identify perfect equilibria for polymatrix games. These results are illustrated on two small game applications. Computational experiments on randomly generated polymatrix games with different size and density are provided.

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Computing a quasi-perfect equilibrium of a two-player game

Cited by 27 publications

References 16 publications

An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information

An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information

Leadership Games: Multiple Followers, Multiple Leaders, and Perfection

On Perfect Nash Equilibria of Polymatrix Games

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