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Symmetries and the complexity of pure Nash equilibrium

Felix Brandt, Felix Fischer, Markus Holzer
2009 Journal of computer and system sciences (Print)  
We investigate the computational complexity of pure Nash equilibria in four classes of symmetric games obtained by considering two additional properties: identical payoff functions for all players and  ...  PLS-hard for the most restricted class for which the existence of a pure equilibrium is guaranteed.  ...  We thank Jan Johannsen for helpful discussions on circuit complexity and local search, and Rob Powers for introducing the first author to the ambiguity of symmetry in games.  ... 
doi:10.1016/j.jcss.2008.09.001 fatcat:ybqpp5eejbci7h47ganirgrxjm

Symmetries and the Complexity of Pure Nash Equilibrium [chapter]

Felix Brandt, Felix Fischer, Markus Holzer
STACS 2007  
We investigate the computational complexity of pure Nash equilibria in four classes of symmetric games obtained by considering two additional properties: identical payoff functions for all players and  ...  PLS-hard for the most restricted class for which the existence of a pure equilibrium is guaranteed.  ...  We thank Jan Johannsen for helpful discussions on circuit complexity and local search, and Rob Powers for introducing the first author to the ambiguity of symmetry in games.  ... 
doi:10.1007/978-3-540-70918-3_19 dblp:conf/stacs/BrandtFH07 fatcat:m5ssfvhed5dnhbg6jkyqo5i7dm

A Catalog of Complexity Classes [chapter]

David S. JOHNSON
1990 Algorithms and Complexity  
J u l y 2 4 , 2 0 0 6 P r e l i m i n a r y D r a f t Symmetries and the Complexity of Pure Nash Equilibrium (Extended Abstract) * Abstract Strategic games may exhibit symmetries in a variety of ways.  ...  Based on these varying notions of symmetry, we investigate the computational complexity of pure Nash equilibria.  ...  Acknowledgements We thank Jan Johannsen for enlightening discussions on circuit complexity and local search, Rob Powers for introducing the first author to the ambiguity of symmetry in games, and Christian  ... 
doi:10.1016/b978-0-444-88071-0.50007-2 fatcat:kh2thwps4vb53m4td54oafuusy

Equilibria of graphical games with symmetries

Felix Brandt, Felix Fischer, Markus Holzer
2011 Theoretical Computer Science  
We establish that deciding the existence of a pure Nash equilibrium is NP-hard in general for all four types.  ...  We thus obtain a natural class of games where the pure equilibrium problem is computationally harder than the mixed equilibrium problem, unless P=NP.  ...  We are grateful to Michael Tautschnig for providing us with a customized version of his ABsolver software.  ... 
doi:10.1016/j.tcs.2010.11.002 fatcat:mbobq35kpbfi7cwtwhynphmuty

Equilibria of Graphical Games with Symmetries [chapter]

Felix Brandt, Felix Fischer, Markus Holzer
2008 Lecture Notes in Computer Science  
We establish that deciding the existence of a pure Nash equilibrium is NP-hard in general for all four types.  ...  We thus obtain a natural class of games where the pure equilibrium problem is computationally harder than the mixed equilibrium problem, unless P=NP.  ...  We are grateful to Michael Tautschnig for providing us with a customized version of his ABsolver software.  ... 
doi:10.1007/978-3-540-92185-1_27 fatcat:xizipxxonbco3gawpcd3wtjg6u

The Complexity of Games on Highly Regular Graphs [chapter]

Konstantinos Daskalakis, Christos H. Papadimitriou
2005 Lecture Notes in Computer Science  
We show that the problem of determining whether such a game on the d-dimensional grid has a pure Nash equilibrium depends on d, and the dichotomy is remarkably sharp: It is in P when d = 1, but NEXP-complete  ...  We study from the complexity point of view the problem of finding equilibria in games defined by highly regular graphs with extremely succinct representation, such as the d-dimensional grid; we argue that  ...  The complexity of Randomized Equilibrium Concepts The complexity of Mixed Nash Equilibria We first give the definition of an automorphism of a game and a symmetric mixed Nash equilibrium and a theorem  ... 
doi:10.1007/11561071_9 fatcat:oaokvpptpzdi5meqf6exnlsxmi

Nash Equilibria in Symmetric Games with Partial Observation

Patricia Bouyer, Nicolas Markey, Steen Vester
2014 Electronic Proceedings in Theoretical Computer Science  
We show several undecidability results, and for bounded-memory strategies, we precisely characterize the complexity of computing pure Nash equilibria (for qualitative objectives) in this game model.  ...  Therefore, this game has partial information and symmetry constraints, which make the computation of Nash equilibria difficult.  ...  We then characterize the complexity of computing (constrained) pure symmetric Nash equilibria in symmetric game structures, when objectives are given as LTL formulas, and when restricting to memoryless  ... 
doi:10.4204/eptcs.146.7 fatcat:vdrrzr3yijbyzkjxzbjiu4cp7q

Pure Nash Equilibria in Online Fair Division

Martin Aleksandrov, Toby Walsh
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
We then focus on pure Nash equilibria of these two mechanisms. Our second main result is that computing a pure Nash equilibrium is tractable for LIKE and intractable for BALANCED LIKE.  ...  The LIKE mechanism is strategy-proof whereas the BALANCED LIKE mechanism is not. Whilst LIKE is strategy-proof, we show that it is not group strategy-proof.  ...  Acknowledgements Data61 (formerly NICTA) is supported by the Australian Government through the Department of Communications and the Australian Research Council through the ICT Centre of Excellence Program  ... 
doi:10.24963/ijcai.2017/7 dblp:conf/ijcai/AleksandrovW17 fatcat:fa33itl6rnbghpuiy47mm6xk4y

Equilibria in a class of aggregative location games

Tobias Harks, Max Klimm
2015 Journal of Mathematical Economics  
We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.  ...  We show that each game in this class possesses a pure Nash equilibrium whenever the players' utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and  ...  Further comments of the attendees of 7th Workshop on Internet and Network Economics and the 13th SAET Conference on Current Trends in Economics are gratefully acknowledged.  ... 
doi:10.1016/j.jmateco.2015.09.006 fatcat:4mf4ogbpc5e2jkg4qo4k625wcy

Pairwise-Interaction Games [chapter]

Martin Dyer, Velumailum Mohanaraj
2011 Lecture Notes in Computer Science  
We study the complexity of computing Nash equilibria in games where players arranged as the vertices of a graph play a symmetric 2-player game against their neighbours.  ...  We analyse this game for n players with a fixed number of actions and show that (1) a mixed Nash equilibrium can be computed in constant time for any game, (2) a pure Nash equilibrium can be computed through  ...  Plausibility of an equilibrium concept like the Nash equilibrium is partly determined by the complexity of computing equilibria [20] .  ... 
doi:10.1007/978-3-642-22006-7_14 fatcat:kmnnpjlkhbah3insyoqtpcwh5m

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  
In particular, we show that even if the action graph is a tree but the number of agent-types is unconstrained, it is NPcomplete to decide the existence of a pure-strategy Nash equilibrium and PPAD-complete  ...  computational complexity of Nash equilibria in the recently proposed model of actiongraph games (AGGs).  ...  Let ν : S → 2 S , We now define a further type of possible symmetry between agents that will be important in our analysis of the complexity of computing Nash equilibria. Definition 1.2.  ... 
doi:10.1137/1.9781611973068.78 fatcat:ad5mrmjj2nhbllu2ndy7zlc5uy

Learning payoff functions in infinite games

Yevgeniy Vorobeychik, Michael P. Wellman, Satinder Singh
2007 Machine Learning  
., symmetry) in the multiagent environment. To measure learning performance, we consider the relative utility of prescribed strategies, rather than the accuracy of payoff functions per se.  ...  We consider a class of games with real-valued strategies and payoff information available only in the form of data from a given sample of strategy profiles.  ...  Moreover, we restrict attention to symmetric games and introduce several forms of aggregation of other agents' actions as another knob for controlling model complexity. 2 The assumption of symmetry allows  ... 
doi:10.1007/s10994-007-0715-8 fatcat:pzarp7vtw5cxrbsmiilwazowci

Page 3363 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
The payoffs are derived from the Nash bargaining solution, and the main results concern the uniqueness of the Nash equilibrium of such a game model, the influence of the commitment tactic on that equilibrium  ...  It deals at the same time with the questions of the complexity of a strategy and of the complexity of finding a strategy.  ... 

Complexity Results about Nash Equilibria [article]

Vincent Conitzer, Tuomas Sandholm
2002 arXiv   pre-print
We also show that 3) determining whether a pure-strategy Bayes-Nash equilibrium exists is NP-hard, and that 4) determining whether a pure-strategy Nash equilibrium exists in a stochastic (Markov) game  ...  Keywords: Nash equilibrium; game theory; computational complexity; noncooperative game theory; normal form game; stochastic game; Markov game; Bayes-Nash equilibrium; multiagent systems.  ...  The question of how complex it is to construct such an equilibrium has been dubbed "a most fundamental computational problem whose complexity is wide open" and "together with factoring, [...] the most  ... 
arXiv:cs/0205074v1 fatcat:xgx22or4kzhpjkyazh2lri2zuq

On the complexity of deciding bimatrix games similarity

Ye Du
2008 Theoretical Computer Science  
Furthermore, it is co-NP-hard to decide whether two bimatrix games have exactly the same set of Nash equilibria.  ...  In this paper, we show that it is NP-complete to decide whether two bimatrix games share a common Nash equilibrium.  ...  I would like to thank Xiaotie Deng for discussions and the anonymous reviewers for their helpful comments.  ... 
doi:10.1016/j.tcs.2008.07.021 fatcat:vlsz3xs3jnc23hbrmjvvj26i7u
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