Distance Hypergraph Polymatrix Coordination Games

We propose the new class of distance hypergraph polymatrix coordination games, properly generalizing distance polymatrix coordination games, in which each subgame can be played by more than two agents. We modelled it using hypergraphs, where each hyperedge represents a subgame played by its agents. Moreover, as for distance polymatrix coordination games, the overall utility of a player x also depends on the payoffs of the subgames where the involved players are far, at most, a given distance from x. As for the original model, we discount these payoffs proportionally by factors depending on the distance of the related hyperedges. We focus on the degradation of the social welfare by resorting to the standard measures of strong Price of Anarchy and Price of Stability for both general and bounded-degree graphs.