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Computing Pure Nash Equilibria via Markov Random Fields [article]

Constantinos Daskalakis
2005 arXiv   pre-print
In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter.  ...  Thus, the problem of deciding whether a graphical game has a pure Nash equilibrium, a well-known intractable problem, can be attacked by well-established algorithms such as Belief Propagation, Junction  ...  Acknowledgements I would like to thank Christos Papadimitriou and Elchanan Mossel for insightful remarks during the preparation of the manuscript.  ... 
arXiv:cs/0510031v1 fatcat:j4hjufcssvd43pbqmlt5tfhct4

Computing pure nash equilibria in graphical games via markov random fields

Constantinos Daskalakis, Christos H. Papadimitriou
2006 Proceedings of the 7th ACM conference on Electronic commerce - EC '06  
We present a reduction from graphical games to Markov random fields so that pure Nash equilibria in the former can be found by statistical inference on the latter.  ...  Our result, when combined with the junction tree algorithm for statistical inference, yields a unified proof of all previously known tractable cases of the NP-complete problem of finding pure Nash equilibria  ...  Nash equilibria and for computing a succinct description of all pure Nash equilibria for large classes of graphical games.  ... 
doi:10.1145/1134707.1134718 dblp:conf/sigecom/DaskalakisP06 fatcat:6oqxrj5t7je4zdbpo5cjtm2mbq

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  
We present a simple Fully Polynomial Time Approximation Scheme for computing mixed Nash equilibria of AGGs with constant degree, constant treewidth and a constant number of agent types (but an arbitrary  ...  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  ...  For a thorough study of the problem of computing pure Nash equilibria in symmetric and anonymous games see [15] .  ... 
doi:10.1137/1.9781611973068.78 fatcat:ad5mrmjj2nhbllu2ndy7zlc5uy

Pure Nash Equilibria: Complete Characterization of Hard and Easy Graphical Games [article]

Albert Xin Jiang, MohammadAli Safari
2010 arXiv   pre-print
We consider the computational complexity of pure Nash equilibria in graphical games.  ...  In particular, we analyze the complexity of PUREGG(C, -), the problem of deciding the existence of pure Nash equilibria in graphical games whose underlying graphs are restricted to class C.  ...  We have focused on the decision problem on the existence of pure Nash equilibria. Related problems include counting the number of pure Nash equilibria and finding one such equilibrium if one exists.  ... 
arXiv:1002.1363v1 fatcat:5mg2u3eq6za4hgxtejrcqt4jmm

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

Constantinos Daskalakis, Grant Schoenebeck, Gregory Valiant, Paul Valiant
2008 arXiv   pre-print
We present a Polynomial Time Approximation Scheme for computing mixed Nash equilibria of AGGs with constant treewidth and a constant number of agent types (and an arbitrary number of strategies), together  ...  We consider the problem of computing Nash Equilibria of action-graph games (AGGs).  ...  We also study the complexity of computing pure Nash equilibria in action graph games with k-types.  ... 
arXiv:0802.1604v1 fatcat:432ggigmgncfda7wlod3hw6rly

Pure Nash Equilibria: Hard and Easy Games

G. Gottlob, G. Greco, F. Scarcello
2005 The Journal of Artificial Intelligence Research  
finding pure Nash and Pareto equilibria is feasible in polynomial time.  ...  We investigate complexity issues related to pure Nash equilibria of strategic games.  ...  P17222-N04 Complementary Approaches to Constraint Satisfaction, and by the GAMES Network of Excellence of the EU. We thank the anonymous referees and Tuomas Sandholm for their very useful comments.  ... 
doi:10.1613/jair.1683 fatcat:txd4gyeer5gw7jjrgbapettkvq

Pure Nash equilibria

Georg Gottlob, Gianluigi Greco, Francesco Scarcello
2003 Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge - TARK '03  
finding pure Nash and Pareto equilibria is feasible in polynomial time.  ...  We investigate complexity issues related to pure Nash equilibria of strategic games.  ...  P17222-N04 Complementary Approaches to Constraint Satisfaction, and by the GAMES Network of Excellence of the EU. We thank the anonymous referees and Tuomas Sandholm for their very useful comments.  ... 
doi:10.1145/846241.846269 dblp:conf/tark/GottlobGS03 fatcat:bfa4tf5mejayjntaqc5tl4ktiy

Pure Nash equilibria

Georg Gottlob, Gianluigi Greco, Francesco Scarcello
2003 Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge - TARK '03  
finding pure Nash and Pareto equilibria is feasible in polynomial time.  ...  We investigate complexity issues related to pure Nash equilibria of strategic games.  ...  P17222-N04 Complementary Approaches to Constraint Satisfaction, and by the GAMES Network of Excellence of the EU. We thank the anonymous referees and Tuomas Sandholm for their very useful comments.  ... 
doi:10.1145/846267.846269 fatcat:rnzcvclg4rg6fehehbbnvmbefq

Public Goods Games in Directed Networks [article]

Christos Papadimitriou, Binghui Peng
2021 arXiv   pre-print
We define general utility public goods games, and prove a complexity dichotomy result for finding pure equilibria, and a PPAD-completeness proof for mixed Nash equilibria.  ...  In contrast, we prove that, in directed networks, a broad range of public goods games have intractable equilibrium problems: The existence of pure Nash equilibria is NP-hard to decide, and mixed Nash equilibria  ...  ACKNOWLEDGMENTS The authors would like to thank Xi Chen and two anonymous EC reviewers for their very helpful feedback.This research was supported by NSF grants CCF-1763970 AF and CCF-1910700 AF, and a  ... 
arXiv:2106.00718v2 fatcat:irkfj4iw6jaqlhxdypukukdavm

Guest Editorial: Special Issue on Parameterized and Exact Computation

Gregory Z. Gutin, Stefan Szeider
2014 Algorithmica  
The paper "Pure Nash Equilibria in Graphical Games and Treewidth" by Antonis Thomas and Jan van Leeuwen explores the role of treewidth the problem of deciding the existence of a Pure Nash Equilibrium in  ...  Bodlaender, and Jesper Nederlof provides an experimental evaluation of the technique of representative sets for the Steiner Tree problem on graphs of small treewidth.  ... 
doi:10.1007/s00453-014-9960-y fatcat:bn3nkk24qvbpda6ja5pz7ondmi

On Finding Pure Nash Equilibria of Discrete Preference Games and Network Coordination Games [article]

Takashi Ishizuka, Naoyuki Kamiyama
2022 arXiv   pre-print
This paper deals with the complexity of the problem of computing a pure Nash equilibrium for discrete preference games and network coordination games beyond O(log n)-treewidth and tree metric spaces.  ...  Finally, we discuss the complexity of finding a pure Nash equilibrium for a two-strategic network coordination game whose cost functions satisfy submodularity.  ...  Acknowledgments This work was supported by JSPS KAKENHI Grant Numbers JP21J10845 and JP20H05795.  ... 
arXiv:2207.01523v1 fatcat:wx7vp4kc5velpjuwm4kbwusj2a

On the complexity of constrained Nash equilibria in graphical games

Gianluigi Greco, Francesco Scarcello
2009 Theoretical Computer Science  
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  ...  equilibria.  ...  However, the strategy in which p 1 , p 2 and p 3 deterministically play a, d, and f , respectively, is a Nash equilibrium. Thus, G 1 admits pure Nash equilibria.  ... 
doi:10.1016/j.tcs.2009.05.030 fatcat:e5fwu7ypxrgpnb7d3umyagi7zm

Single Parameter FPT-Algorithms for Non-trivial Games [chapter]

Vladimir Estivill-Castro, Mahdi Parsa
2011 Lecture Notes in Computer Science  
However, this paper provides positive results regarding Nash equilibria.  ...  Moreover, we show that, although NP-Complete, the problem of Best Nash Equilibrium is also fix-parameter tractable.  ...  We used the link between graph theory and Nash equilibria to show our FPT results.  ... 
doi:10.1007/978-3-642-19222-7_13 fatcat:uzq2zj5kqrejzo5s62usgba2nu

On Sparse Discretization for Graphical Games [article]

Luis E. Ortiz
2014 arXiv   pre-print
This short paper concerns discretization schemes for representing and computing approximate Nash equilibria, with emphasis on graphical games, but briefly touching on normal-form and poly-matrix games.  ...  for computing approximate Nash equilibria; (2) to summarize the state-of-the-art on computing approximate Nash equilibria, with emphasis on relevance to graphical games; (3) to help clarify the distinction  ...  There exists a PTAS for computing an approximate Nash equilibria in nplayer GGs with bounded maximum number of actions, bounded neighborhood size and primal-graph treewidth w ′ = O(log(n)).  ... 
arXiv:1411.3320v1 fatcat:laaiabavarfxfjsoo4govexunu

Computing Constrained Approximate Equilibria in Polymatrix Games [article]

Argyrios Deligkas and John Fearnley and Rahul Savani
2017 arXiv   pre-print
In the second part, we provide a deterministic QPTAS for interaction graphs with bounded treewidth and with logarithmically many actions per player that can compute constrained approximate equilibria for  ...  This paper is about computing constrained approximate Nash equilibria in polymatrix games, which are succinctly represented many-player games defined by an interaction graph between the players.  ...  Constrained approximate Nash equilibria One variable decomposable constraints. We now adapt the algorithm to find a certain class of constrained approximate Nash equilibria.  ... 
arXiv:1705.02266v2 fatcat:edbo2ygjezchjmilnzj43673yi
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