Efficient Local Search in Coordination Games on Graphs
Sunil Simon, Dominik Wojtczak

TL;DR
This paper investigates the existence and efficient computation of pure Nash and strong equilibria in coordination games on specific classes of graphs, providing polynomial-time algorithms for certain graph classes and showing limitations in generalizations.
Contribution
It identifies graph classes where finite improvement paths lead to equilibria in polynomial time and demonstrates the optimality of these results.
Findings
Polynomial-time algorithms for equilibria in certain graph classes
Existence of equilibria in DAGs and cliques
Limitations in general graph classes
Abstract
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…
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Taxonomy
TopicsGame Theory and Applications · Game Theory and Voting Systems · Experimental Behavioral Economics Studies
