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Symmetries and the complexity of pure Nash equilibrium

2009
*
Journal of computer and system sciences (Print)
*

We investigate

doi:10.1016/j.jcss.2008.09.001
fatcat:ybqpp5eejbci7h47ganirgrxjm
*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. ...##
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Symmetries and the Complexity of Pure Nash Equilibrium
[chapter]

*
STACS 2007
*

We investigate

doi:10.1007/978-3-540-70918-3_19
dblp:conf/stacs/BrandtFH07
fatcat:m5ssfvhed5dnhbg6jkyqo5i7dm
*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. ...##
###
A Catalog of Complexity Classes
[chapter]

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

doi:10.1016/b978-0-444-88071-0.50007-2
fatcat:kh2thwps4vb53m4td54oafuusy
*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 ...##
###
Equilibria of graphical games with symmetries

2011
*
Theoretical Computer Science
*

We establish that deciding

doi:10.1016/j.tcs.2010.11.002
fatcat:mbobq35kpbfi7cwtwhynphmuty
*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. ...##
###
Equilibria of Graphical Games with Symmetries
[chapter]

2008
*
Lecture Notes in Computer Science
*

We establish that deciding

doi:10.1007/978-3-540-92185-1_27
fatcat:xizipxxonbco3gawpcd3wtjg6u
*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. ...##
###
The Complexity of Games on Highly Regular Graphs
[chapter]

2005
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/11561071_9
fatcat:oaokvpptpzdi5meqf6exnlsxmi
*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 ...##
###
Nash Equilibria in Symmetric Games with Partial Observation

2014
*
Electronic Proceedings in Theoretical Computer Science
*

We show several undecidability results,

doi:10.4204/eptcs.146.7
fatcat:vdrrzr3yijbyzkjxzbjiu4cp7q
*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 ...##
###
Pure Nash Equilibria in Online Fair Division

2017
*
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
*

We then focus on

doi:10.24963/ijcai.2017/7
dblp:conf/ijcai/AleksandrovW17
fatcat:fa33itl6rnbghpuiy47mm6xk4y
*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 ...##
###
Equilibria in a class of aggregative location games

2015
*
Journal of Mathematical Economics
*

We also provide examples exhibiting that, if one

doi:10.1016/j.jmateco.2015.09.006
fatcat:4mf4ogbpc5e2jkg4qo4k625wcy
*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. ...##
###
Pairwise-Interaction Games
[chapter]

2011
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/978-3-642-22006-7_14
fatcat:kmnnpjlkhbah3insyoqtpcwh5m
*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] . ...##
###
On the Complexity of Nash Equilibria of Action-Graph Games
[chapter]

2009
*
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

In particular, we show that even if

doi:10.1137/1.9781611973068.78
fatcat:ad5mrmjj2nhbllu2ndy7zlc5uy
*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. ...##
###
Learning payoff functions in infinite games

2007
*
Machine Learning
*

.,

doi:10.1007/s10994-007-0715-8
fatcat:pzarp7vtw5cxrbsmiilwazowci
*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 ...##
###
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]

2002
*
arXiv
*
pre-print

We also show that 3) determining whether a

arXiv:cs/0205074v1
fatcat:xgx22or4kzhpjkyazh2lri2zuq
*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 ...##
###
On the complexity of deciding bimatrix games similarity

2008
*
Theoretical Computer Science
*

Furthermore, it is co-NP-hard to decide whether two bimatrix games have exactly

doi:10.1016/j.tcs.2008.07.021
fatcat:vlsz3xs3jnc23hbrmjvvj26i7u
*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. ...
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