Graphical potential games

Abstract

We study the class of potential games that are also graphical games with respect to a given graph G of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on G. From this characterization, and from the Hammersley–Clifford theorem, it follows that the potentials of such games can be decomposed into local potentials.

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