The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Filters
Games of fixed rank: A hierarchy of bimatrix games
[article]
2005
arXiv
pre-print
Preserved Fulltext
Specifically, we investigate a hierarchy of bimatrix games (A,B) which results from restricting the rank of the matrix A+B to be of fixed rank at most k. ...
For every fixed k, this class strictly generalizes the class of zero-sum games, but is a very special case of general bimatrix games. ...
Although the problem of finding a Nash equilibrium in a game of fixed rank is a very special case of the problem of finding a Nash equilibrium in an arbitrary bimatrix game, we do not know if there exists ...
arXiv:cs/0511021v1
fatcat:6bzfl6h6e5cynlodqflzeax2za
Games of fixed rank: a hierarchy of bimatrix games
2009
Economic Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2011; you can also visit the original URL.
The file type is application/pdf.
We propose and investigate a hierarchy of bimatrix games (A, B), whose (entry-wise) sum of the pay-off matrices of the two players is of rank k, where k is a constant. ...
We will say the rank of such a game is k. For every fixed k, the class of rank kgames strictly generalizes the class of zero-sum games, but is a very special case of general bimatrix games. ...
From the viewpoint of game theory, it provides a flexible hierarchy between zero-sum games and general bimatrix games. ...
doi:10.1007/s00199-009-0436-2
fatcat:srt5zgxqwbfcnppfvvwvg6qsi4
Enumerating the Nash equilibria of rank 1-games
[article]
2007
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
A bimatrix game (A,B) is called a game of rank k if the rank of the matrix A+B is at most k. We consider the problem of enumerating the Nash equilibria in (non-degenerate) games of rank 1. ...
game of rank 1. ...
ENUMERATING THE NASH EQUILIBRIA OF RANK 1-GAMES ...
arXiv:0709.1263v1
fatcat:wktlp4xtardbjepgs6bocza7ru
Enumerating the Nash equilibria of rank-1 games
[chapter]
2009
CRM Proceedings and Lecture notes AMS
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
A bimatrix game (A, B) is called a game of rank k if the rank of the matrix A + B is at most k. We consider the problem of enumerating the Nash equilibria in (non-degenerate) games of rank 1. ...
game of rank 1. ...
Recently, Kannan and Theobald [9] have introduced a hierarchy of bimatrix games in which the matrix A + B is restricted to be of rank at most k, for some fixed constant k. ...
doi:10.1090/crmp/048/06
fatcat:ep4dn2oki5hx3jbhqhrgcgwasi
Bilinear Games: Polynomial Time Algorithms for Rank Based Subclasses
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We consider a rank based hierarchy of bilinear games, where rank of a game (A,B) is defined as rank(A+B). ...
(ET'09), for bimatrix games with low rank matrices. ...
Next, we extend Kannan and Theobald's [17] rank-based hierarchy for bimatrix games to bilinear games, by defining the rank of a bilinear game with payoff matrices (A, B) as the rank of (A + B). ...
arXiv:1109.6182v1
fatcat:cuairizybbhvzjmvb3d7dgalgy
Fast Algorithms for Rank-1 Bimatrix Games
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The rank of a bimatrix game is the matrix rank of the sum of the two payoff matrices. ...
In contrast, such a path-following method finds only one equilibrium of a bimatrix game. (4) The number of equilibria of a rank-1 game may be exponential. (5) There is a homeomorphism between the space ...
We thank two anonymous referees of Operations Research for their detailed comments which helped improve the manuscript. Heinrich Nax suggested the "trade game" (70) in Section 10. ...
arXiv:1812.04611v4
fatcat:3yepxkylvjacreouuxdcoztuam
Rank-1 Bi-matrix Games: A Homeomorphism and a Polynomial Time Algorithm
[article]
2010
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Further, we extend the rank-1 homeomorphism result to a fixed rank game space, and give a fixed point formulation on [0,1]^k for solving a rank-k game. ...
Given a rank-1 bimatrix game (A,B), i.e., where rank(A+B)=1, we construct a suitable linear subspace of the rank-1 game space and show that this subspace is homeomorphic to its Nash equilibrium correspondence ...
Kannan and Theobald [8] defined a hierarchy of bimatrix games using the rank of (A + B) and gave a polynomial time algorithm to compute an approximate Nash equilibrium for games of a fixed rank k. ...
arXiv:1010.3083v2
fatcat:dnmsy2qeabhblogfnnybwl7z3a
Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses
[chapter]
2010
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
It is though incomparable to the subclass of games with fixed rank [16]: Even rank−1 games may not be mutually concave (eg, Prisoner's dilemma), but on the other hand, there exist mutually concave games ...
This subclass entirely contains the most popular subclass of polynomial-time solvable bimatrix games, namely, all the constantsum games (rank−0 games). ...
[16] introduced a hierarchy of the bimatrix games, according to the rank of the matrix R + C of the game R, C , which was called the rank of the game. ...
doi:10.1007/978-3-642-15369-3_24
fatcat:ukvdyvu6qffhrhkm3tfyeuvrtm
On mutual concavity and strategically-zero-sum bimatrix games
2012
Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We conclude our discussion with a comparison of MC-games (or, SZS-games) to k-rank games, which are known to admit for 2NASH a FPTAS when k is fixed [18] , and a polynomialtime algorithm for k = 1 [2]. ...
between the spaces of CE and NE points in a bimatrix game (e.g., [15, 26, 33] ). ...
We also observed that the class of MC-games, which entirely contains all constant-sum games, is incomparable to the class of bimatrix games with fixed rank: even rank-1 games may be non-MC-games, and even ...
doi:10.1016/j.tcs.2012.01.016
fatcat:ihoq65e2nzdlpfv3nyhpujdnfa
Semidefinite Programming and Nash Equilibria in Bimatrix Games
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2018 pre-print arXiv:1706.08550v2 fatcat:2rf3vs7eina45pao5gpmvr7vwmOther Versions
We explore the power of semidefinite programming (SDP) for finding additive epsilon-approximate Nash equilibria in bimatrix games. ...
Furthermore, we prove that if a rank-2 solution to our SDP is found, then a 5/11-NE can be recovered for any game, or a 1/3-NE for a symmetric game. ...
equilibria of a bimatrix game. ...
arXiv:1706.08550v3
fatcat:5zwr6lcukbhu3m3fvv54zba2ri
A Semidefinite Hierarchy for Disjointly Constrained Multilinear Programming
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
For nondegenerate bimatrix games, a Nash equilibrium can be computed by the sum of squares approach in finitely many steps. ...
Based on a reformulation of the problem in terms of sum-of-squares polynomials, we study a hierarchy of semidefinite relaxations to the problem. ...
Originally, bilinear programming has been considered as a generalization of bimatrix games in game theory. ...
arXiv:1603.03634v1
fatcat:happcknkmzacfbb4q2c774zxky
A Polynomial-Time Algorithm for 1/2-Well-Supported Nash Equilibria in Bimatrix Games
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Since the seminal PPAD-completeness result for computing a Nash equilibrium even in two-player games, an important line of research has focused on relaxations achievable in polynomial time. ...
Our algorithm is based on linear programming and in particular on exploiting suitably defined zero-sum games that arise from the payoff matrices of the two players. ...
Observe that for any fixed value of k, the size of the support of a k-uniform strategy is at most k. This implies that in a n × n bimatrix game, there are at most O(n k ) kuniform strategy profiles. ...
arXiv:2207.07007v1
fatcat:hukr5lrbnzg4dlreeilyagyvqi
Exchangeable Equilibria, Part I: Symmetric Bimatrix Games
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We introduce the notion of exchangeable equilibria of a symmetric bimatrix game, defined as those correlated equilibria in which players' strategy choices are conditionally independently and identically ...
We give several game-theoretic interpretations and a version of the "revelation principle". ...
This research was funded by the National Science Foundation under Award 1027922 and the Air Force Office of Scientific Research under grant FA9550-11-1-0305. ...
arXiv:1307.3586v3
fatcat:46yq7yo7dvcvfpkb66t5afy6lm
Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
We consider a series of canonical bimatrix games and an ensemble of random performance functions that demonstrate the generality of our mechanism, even when faced with highly cyclic games. ...
To test that theory, we run a series of evolution experiments designed to mimic genetic training algorithms. ...
These include a set of illustrative bimatrix games, and a sequence of randomly generated games with tuneable structure designed to demonstrate generality. ...
arXiv:2205.08015v1
fatcat:jwjzw3o4gzdkbo5f2jylzajy3q
Complexity Aspects of Fundamental Questions in Polynomial Optimization
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We show that for a symmetric game, a 1/3-Nash equilibrium can be efficiently recovered from any rank-2 solution to this relaxation. ...
We also give a new characterization of coercive polynomials that lends itself to a hierarchy of SDPs. ...
quadratic objective function over the set of Nash equilibria of a bimatrix game. ...
arXiv:2008.12170v1
fatcat:jdlr2ydcorcg3gmxhwhhcjngmq
« Previous
Showing results 1 — 15 out of 65 results