Multipotential Games

Abstract

We introduce and analyze q -potential games and q -congestion games, where q is a positive integer. A 1-potential (congestion) game is a potential (congestion) game. We show that a game is a q -potential game if and only if it is (up to an isomorphism) a q -congestion game. As a corollary, we derive the result that every game in strategic form is a q -congestion game for some q . It is further shown that every q -congestion game is isomorphic to a q -network game, where the network environment is defined by a directed graph with one origin and one destination. Finally we discuss our main agenda: The issue of representing q -congestion games with non-negative cost functions by congestion models with non-negative and monotonic facility cost functions. We provide some initial results in this regard.