Unit vector games

Savani, Rahul; Stengel, Bernhard von

doi:10.1111/ijet.12077

Cited by 6 publications

(2 citation statements)

References 28 publications

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“…We denote these games as Tournament. -Unit Vector Games (UVG) [18]. The payoffs for the column player are chosen randomly from the range [0, 1], but for the row player each column j contains exactly one 1 payoff with the rest being 0.…”

Section: Cournotduopolymentioning

confidence: 99%

An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

Fearnley

Igwe

Savani

2015

Experimental Algorithms

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Abstract. While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares a number of approximation methods and exact methods. In particular, we explore the trade-off between the quality of approximate equilibrium and the required running time to find one. We found that the existing library GAMUT, which has been the de facto standard that has been used to test exact methods, is insufficient as a test bed for approximation methods since many of its games have pure equilibria or other easy-to-find good approximate equilibria. We extend the breadth and depth of our study by including new interesting families of bimatrix games, and studying bimatrix games upto size 2000×2000. Finally, we provide new close-to-worst-case examples for the best-performing algorithms for finding approximate Nash equilibria.

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Section: Cournotduopolymentioning

confidence: 99%

An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

Fearnley

Igwe

Savani

2015

Experimental Algorithms

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“…Cyclic polytopes are the analogues of convex polygons in higher dimensions [Gal63]. For this reason, cyclic polytopes possess important properties [McM70] and are found in many areas of mathematics, such as higher category theory and algebraic K-theory [KV91, DK19b, Pog17, DJW19], as well as game theory [SvS06,SvS16].…”

Section: Introductionmentioning

confidence: 99%

New interpretations of the higher Stasheff--Tamari orders

Williams¹

2020

Preprint

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In 1996, Edelman and Reiner defined the two higher Stasheff-Tamari orders on triangulations of cyclic polytopes and conjectured them to coincide. We open up an algebraic angle for approaching this conjecture by showing how these orders arise naturally in the representation theory of the higher Auslander algebras of type A, denoted A d n . For this we give new combinatorial interpretations of the orders, making them comparable. We then translate these combinatorial interpretations into the algebraic framework. We also show how triangulations of odd-dimensional cyclic polytopes arise in the representation theory of A d n , namely as equivalence classes of maximal green sequences. We furthermore give the odddimensional counterpart to the known description of 2d-dimensional triangulations as sets of non-intersecting d-simplices of a maximal size. This consists in a definition of two new properties which imply that a set of d-simplices produces a (2d + 1)-dimensional triangulation.

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Nash equilibria in random games with right fat-tailed distributions

Pei

Takahashi

2023

Int J Game Theory

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Unit vector games

Cited by 6 publications

References 28 publications

An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

New interpretations of the higher Stasheff--Tamari orders

Nash equilibria in random games with right fat-tailed distributions

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