Filters








953 Hits in 4.5 sec

The computational complexity of nash equilibria in concisely represented games

Grant Schoenebeck, Salil Vadhan
2006 Proceedings of the 7th ACM conference on Electronic commerce - EC '06  
Games may be represented in many different ways, and different representations of games affect the complexity of problems associated with games, such as finding a Nash equilibrium.  ...  We study two models of concisely represented games: circuit games, where the payoffs are computed by a given boolean circuit, and graph games, where each agent's payoff is a function of only the strategies  ...  Acknowledgments We thank Eli Ben-Sasson, Adam Klivans, Ryan O'Donnell, Rocco Servedio, and Amir Shpilka for many discussions about algorithmic aspects of Nash equilibria which informed this work.  ... 
doi:10.1145/1134707.1134737 dblp:conf/sigecom/SchoenebeckV06 fatcat:lzin6ftnivfalfafketbzmm6ai

The Computational Complexity of Nash Equilibria in Concisely Represented Games

Grant R. Schoenebeck, Salil Vadhan
2012 ACM Transactions on Computation Theory  
Games may be represented in many different ways, and different representations of games affect the complexity of problems associated with games, such as finding a Nash equilibrium.  ...  We study two models of concisely represented games: circuit games, where the payoffs are computed by a given boolean circuit, and graph games, where each agent's payoff is a function of only the strategies  ...  Acknowledgments We thank Eli Ben-Sasson, Adam Klivans, Ryan O'Donnell, Rocco Servedio, and Amir Shpilka for many discussions about algorithmic aspects of Nash equilibria which informed this work.  ... 
doi:10.1145/2189778.2189779 fatcat:vihzmfqrrbhwtci7o5bqbhtsxq

Correlated equilibria in graphical games

Sham Kakade, Michael Kearns, John Langford, Luis Ortiz
2003 Proceedings of the 4th ACM conference on Electronic commerce - EC '03  
We examine correlated equilibria in the recently introduced formalism of graphical games, a succinct representation for multiplayer games.  ...  Our first main result establishes that this Markov network succinctly represents all correlated equilibria of the graphical game up to expected payoff equivalence.  ...  ACKNOWLEDGEMENTS We give warm thanks to Dean Foster for numerous helpful discussions, and to Stuart Geman for his help with the proof of Lemma 3.  ... 
doi:10.1145/779928.779934 dblp:conf/sigecom/KakadeKLO03 fatcat:vaifykxajfdx5cgxwlu7t32cl4

Bounds for the Query Complexity of Approximate Equilibria

Paul W. Goldberg, Aaron Roth
2016 ACM Transactions on Economics and Computation  
This gives a polynomial-query algorithm for computing well supported approximate Nash equilibria (and hence correlated equilibria) in concisely represented games.  ...  We analyze the number of payoff queries needed to compute approximate equilibria of multi-player games.  ...  Since verifying equilibria can be done query efficiently, this gives query efficient algorithms for computing approximate well supported equilibria in concisely represented games.  ... 
doi:10.1145/2956582 fatcat:efx5k4chcfh2njriookkml735e

Bounds for the query complexity of approximate equilibria

Paul W. Goldberg, Aaron Roth
2014 Proceedings of the fifteenth ACM conference on Economics and computation - EC '14  
This gives a polynomial-query algorithm for computing well supported approximate Nash equilibria (and hence correlated equilibria) in concisely represented games.  ...  We analyze the number of payoff queries needed to compute approximate equilibria of multi-player games.  ...  Since verifying equilibria can be done query efficiently, this gives query efficient algorithms for computing approximate well supported equilibria in concisely represented games.  ... 
doi:10.1145/2600057.2602845 dblp:conf/sigecom/GoldbergR14 fatcat:h7wplw4vlzhllntngd6t55cpoi

Complexity Results about Nash Equilibria [article]

Vincent Conitzer, Tuomas Sandholm
2002 arXiv   pre-print
Nash equilibria (or connected sets of Nash equilibria).  ...  Keywords: Nash equilibrium; game theory; computational complexity; noncooperative game theory; normal form game; stochastic game; Markov game; Bayes-Nash equilibrium; multiagent systems.  ...  There has been growing interest in the computational complexity of natural questions in game theory.  ... 
arXiv:cs/0205074v1 fatcat:xgx22or4kzhpjkyazh2lri2zuq

Solution Concepts in A-Loss Recall Games: Existence and Computational Complexity [article]

Jiri Cermak and Branislav Bosansky and Michal Pechoucek
2017 arXiv   pre-print
However, most of the algorithmic results are negative for imperfect recall games -- a Nash equilibrium~(NE) does not have to exist and computing a best response or a maxmin strategy is NP-hard.  ...  The importance of imperfect recall games stems from allowing a concise representation of strategies compared to perfect recall games where players remember all information.  ...  This research was supported by the Czech Science Foundation (grant no. 15-23235S) and by the Grant Agency of the Czech Technical University in Prague, grant No. SGS16/235/OHK3/3T/13.  ... 
arXiv:1608.01500v3 fatcat:cvlabrc27bfo3eyav2juj6bdta

A Survey of PPAD-Completeness for Computing Nash Equilibria [article]

Paul W. Goldberg
2011 arXiv   pre-print
The most well-known such problem is that of computing a Nash equilibrium of a game. Other examples include the search for market equilibria, and envy-free allocations in the context of cake-cutting.  ...  In this paper, I give a relatively informal overview of the proofs used in the PPAD-completeness results. The focus is on the mixed Nash equilibria guaranteed to exist by Nash's theorem.  ...  [20] show that most standard classes of concisely-represented games (such as graphical games and polymatrix games) have equilibrium computation problems that reduce to 2-Nash and so belong to PPAD.  ... 
arXiv:1103.2709v2 fatcat:xopz6wzhwnbqln4krtc6v5iwze

Computational Complexity of Approximate Nash Equilibrium in Large Games [article]

Aviad Rubinstein
2014 arXiv   pre-print
We prove that finding an epsilon-Nash equilibrium in a succinctly representable game with many players is PPAD-hard for constant epsilon.  ...  Our proof uses succinct games, i.e. games whose payoff function is represented by a circuit. Our techniques build on a recent query complexity lower bound by Babichenko.  ...  Related works Schoenebeck and Vadhan [20] studied comprehensively the computational complexity of Nash Equilibria in succinct games and other concise representations.  ... 
arXiv:1405.0524v3 fatcat:q33sizzt4bf75ddde365kxyp3i

Nash Equilibria, the Price of Anarchy and the Fully Mixed Nash Equilibrium Conjecture [chapter]

Martin Gairing, Thomas Lücking, Burkhard Monien, Karsten Tiemann
2005 Lecture Notes in Computer Science  
Koutsoupias and Papadimitriou [21] were not only interested in the computational complexity of Nash equilibria but also in the degradation of the social welfare of the system due to the selfish behavior  ...  Though the celebrated results of Nash [30, 31] ensure the existence of a mixed Nash equilibrium, the complexity to compute such a Nash equilibrium is widely unknown.  ...  After a formal definition of (weighted) congestion games in Section 2, we turn our attention to the existence and computational complexity of pure Nash equilibria in Section 3.  ... 
doi:10.1007/11523468_5 fatcat:imivbt76zvc6nlmsao6tvrrgli

Graphical Games [chapter]

Michael Kearns
2008 The New Palgrave Dictionary of Economics  
In this chapter we examine the representational and algorithmic aspects of a class of graph-theoretic models for multiplayer games.  ...  In addition to a number of nice computational properties, these models have close connections to well-studied graphical models for probabilistic inference in machine learning and statistics.  ...  ., 2001) for presentation in this chapter. Bibliography  ... 
doi:10.1057/978-1-349-95121-5_2123-1 fatcat:rtozhhbbzzdevnttq5ixebokwa

On the Complexity of Nash Equilibria of Action-Graph Games [chapter]

Constantinos Daskalakis, Grant Schoenebeckt, Gregory Valiant, Paul Valiant
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
computational complexity of Nash equilibria in the recently proposed model of actiongraph games (AGGs).  ...  In light of much recent interest in finding a model of multi-player multi-action games that allows for efficient computation of Nash equilibria yet remains as expressive as possible, we investigate the  ...  Our Results We examine, and largely resolve the computational complexity of computing Nash equilibria in action graph games.  ... 
doi:10.1137/1.9781611973068.78 fatcat:ad5mrmjj2nhbllu2ndy7zlc5uy

PPAD-Complete Pure Approximate Nash Equilibria in Lipschitz Games [article]

Paul W. Goldberg, Matthew J. Katzman
2022 arXiv   pre-print
Here we provide the first hardness result for the corresponding computational problem, showing that even for a simple class of Lipschitz games (Lipschitz polymatrix games), finding pure ϵ-approximate equilibria  ...  They showed via the probabilistic method that n-player Lipschitz games with m strategies per player have pure ϵ-approximate Nash equilibria, for ϵ≥λ√(8nlog(2mn)).  ...  This leaves open the problem of computing an equilibrium of a Lipschitz game that has a concise representation: if a game is known to be concisely representable, then its query complexity is low [19]  ... 
arXiv:2207.09962v1 fatcat:xttfkairtrd5vl3nwr7th4rjge

Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games [article]

Paul W. Goldberg, Matthew J. Katzman
2021 arXiv   pre-print
Finally, we provide an exponential lower bound on the deterministic query complexity of finding ϵ-approximate correlated equilibria of n-player, m-action, λ-Lipschitz games for strong values of ϵ, motivating  ...  They showed that such games admit ϵ-approximate pure Nash equilibria for certain settings of ϵ and λ. They left open, however, the question of how hard it is to find such an equilibrium.  ...  Acknowledgements We thank Francisco Marmalejo Cossío and Rahul Santhanam for their support in the development of this work, and the reviewers of an earlier version for helpful comments.  ... 
arXiv:2107.03898v1 fatcat:vdkkgxj6irfktcgkwf7hivl4si

On the complexity of constrained Nash equilibria in graphical games

Gianluigi Greco, Francesco Scarcello
2009 Theoretical Computer Science  
Based on this framework, the complexity of deciding the existence and of computing constrained equilibria is then investigated, in the light of evidencing how the intrinsic difficulty of these tasks is  ...  In particular, for this latter case, restrictions on players' interactions and on constraints are identified, that make the computation of Nash equilibria an easy problem, for which polynomial and highlyparallelizable  ...  This problem has recently been attacked by Schoenebeck and Vadhan [53, 54] , who undertake a systematic study of the complexity of Nash equilibria in concisely represented games, by focusing, in particular  ... 
doi:10.1016/j.tcs.2009.05.030 fatcat:e5fwu7ypxrgpnb7d3umyagi7zm
« Previous Showing results 1 — 15 out of 953 results