A common generalization of budget games and congestion games

Abstract

Budget games were introduced by Drees, Riechers, and Skopalik (2014) as a model of noncooperative games arising from resource allocation problems. Budget games have several similarities to congestion games, one of which is that the matroid structure of the strategy space is essential for the existence of a pure Nash equilibrium (PNE). Despite these similarities, however, the theoretical relation between budget games and congestion games has been unclear. In this paper, we provide a common generalization of budget games and congestion games, called generalized budget games (g-budget games, for short), to establish a large class of noncooperative games retaining the nice property of the matroid structure. We show that the model of g-budget games includes weighted congestion games and player-specific congestion games under certain assumptions. We further show that g-budget games also include offset budget games, a generalized model of budget games by Drees, Feldotto, Riechers, and Skopalik (2019). We then prove that every matroid g-budget game has a PNE, which extends the result for budget games. We finally a PNE in a certain class of singleton g-budget games can be computed in a greedy manner.