Efficient Local Search in Coordination Games on Graphs Article Swipe

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YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1604.04809

We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. Prior work shows that the problem of determining the existence of a pure Nash equilibrium for these games is NP-complete already for graphs with all weights equal to one and no bonuses. However, for several classes of graphs (e.g. DAGs and cliques) pure Nash equilibria or even strong equilibria always exist and can be found by simply following a particular improvement or coalition-improvement path, respectively. In this paper we identify several natural classes of graphs for which a finite improvement or coalition-improvement path of polynomial length always exists, and, as a consequence, a Nash equilibrium or strong equilibrium in them can be found in polynomial time. We also argue that these results are optimal in the sense that in natural generalisations of these classes of graphs, a pure Nash equilibrium may not even exist.

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Nash equilibrium Best response Epsilon-equilibrium Mathematical economics Stochastic game Correlated equilibrium Mathematics Path (computing) Risk dominance Strategy Combinatorics Game theory Mathematical optimization Equilibrium selection Computer science Repeated game Programming language

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Type: article
Language: en
Landing Page: http://arxiv.org/abs/1604.04809
PDF: https://arxiv.org/pdf/1604.04809
OA Status: green
Cited By: 5
References: 18
Related Works: 20
OpenAlex ID: https://openalex.org/W2338333704

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DOI: https://doi.org/10.48550/arxiv.1604.04809

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Title: Efficient Local Search in Coordination Games on Graphs

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Type: article

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Language: en

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Publication year: 2016

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Publication date: 2016-04-16

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Authors: Sunil Simon, Dominik Wojtczak

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Landing page: https://arxiv.org/abs/1604.04809

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Concepts: Nash equilibrium, Best response, Epsilon-equilibrium, Mathematical economics, Stochastic game, Correlated equilibrium, Mathematics, Path (computing), Risk dominance, Strategy, Combinatorics, Game theory, Mathematical optimization, Equilibrium selection, Computer science, Repeated game, Programming language

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Cited by: 5

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Citations by year (recent): 2021: 1, 2018: 1, 2017: 2, 2016: 1

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abstract_inverted_index.Prior	57
abstract_inverted_index.These	43
abstract_inverted_index.argue	165
abstract_inverted_index.bonus	37
abstract_inverted_index.chose	28
abstract_inverted_index.edges	24
abstract_inverted_index.equal	83
abstract_inverted_index.exist	107
abstract_inverted_index.fixed	35
abstract_inverted_index.found	111, 159
abstract_inverted_index.games	3, 44, 74
abstract_inverted_index.given	41
abstract_inverted_index.paper	124
abstract_inverted_index.path,	120
abstract_inverted_index.sense	173
abstract_inverted_index.shows	59
abstract_inverted_index.study	1
abstract_inverted_index.these	73, 167, 179
abstract_inverted_index.time.	162
abstract_inverted_index.where	8
abstract_inverted_index.which	133
abstract_inverted_index.always	106, 143
abstract_inverted_index.common	55
abstract_inverted_index.exist.	190
abstract_inverted_index.finite	135
abstract_inverted_index.graphs	79, 94, 131
abstract_inverted_index.length	142
abstract_inverted_index.payoff	10
abstract_inverted_index.player	13
abstract_inverted_index.simply	113
abstract_inverted_index.strong	104, 153
abstract_inverted_index.absence	52
abstract_inverted_index.already	77
abstract_inverted_index.capture	45
abstract_inverted_index.classes	92, 129, 180
abstract_inverted_index.defined	15
abstract_inverted_index.exists,	144
abstract_inverted_index.graphs,	7, 182
abstract_inverted_index.natural	128, 176
abstract_inverted_index.optimal	170
abstract_inverted_index.picking	39
abstract_inverted_index.players	26
abstract_inverted_index.problem	62
abstract_inverted_index.results	168
abstract_inverted_index.several	91, 127
abstract_inverted_index.weights	21, 82
abstract_inverted_index.However,	89
abstract_inverted_index.bonuses.	88
abstract_inverted_index.cliques)	98
abstract_inverted_index.directed	6
abstract_inverted_index.globally	54
abstract_inverted_index.identify	126
abstract_inverted_index.strategy	31
abstract_inverted_index.weighted	5
abstract_inverted_index.augmented	32
abstract_inverted_index.existence	66
abstract_inverted_index.following	114
abstract_inverted_index.strategic	2
abstract_inverted_index.strategy.	42
abstract_inverted_index.equilibria	101, 105
abstract_inverted_index.particular	116
abstract_inverted_index.polynomial	141, 161
abstract_inverted_index.NP-complete	76
abstract_inverted_index.determining	64
abstract_inverted_index.equilibrium	71, 151, 154, 186
abstract_inverted_index.improvement	117, 136
abstract_inverted_index.strategies.	56
abstract_inverted_index.consequence,	148
abstract_inverted_index.coordination	49
abstract_inverted_index.non-negative	36
abstract_inverted_index.respectively.	121
abstract_inverted_index.generalisations	177
abstract_inverted_index.coalition-improvement	119, 138
cited_by_percentile_year
countries_distinct_count	2
institutions_distinct_count	2
citation_normalized_percentile