Generalized Distance Polymatrix Games (short paper)

We propose a new class of generalized distance polymatrix games, which extends distance polymatrix coordination games by allowing each subgame to be played by more than two agents. These games can be effectively modeled using hypergraphs, where each hyperedge represents a subgame played by its agents. Similar to distance polymatrix coordination games, the overall utility of a player 𝑥 depends on the payoffs of subgames involving players within a certain distance from 𝑥. As in the original model, these payoffs are discounted proportionally by factors that depend on the distance of the corresponding hyperedges. After formalizing and motivating our model, we investigate the existence of exact and approximate strong equilibria. We also examine the degradation of social welfare using the standard measures of the Price of Anarchy and the Price of Stability, both for general and bounded-degree hypergraphs.