2026/07/27 by Francesca Albertini, Paolo Dai Pra
Decision Sciences · Physics and Astronomy · Social Sciences · #Evolutionary Game Theory and Cooperation #Game Theory and Applications #Opinion Dynamics and Social Influence
paper · doi:10.1137/24m1697451
openalex publication_date 2026/07/27 · openalex created_date 2026/07/28 · openalex updated_date 2026/07/28
Abstract. We consider [Formula: see text]-player games, in continuous time, finite state space, and finite time horizon, on a geometrical structure possessing a macroscopic limit in a suitable sense. This geometrical structure breaks the permutation invariance property that gives rise to mean field games. The corresponding limit game is a variant of mean field games that we call a long range game. We prove that this asymptotic scheme satisfies the following key properties: (a) the long range game admits at least one equilibrium; (b) this equilibrium is unique under a suitable monotonicity condition; (c) the feedback corresponding to any equilibrium of the long range game is a quasi-Nash equilibrium for the [Formula: see text]-player games. We finally show that this scheme includes several examples of interaction mechanisms, in particular, Kac-type interactions and interactions on generalized Erdös–Renyi graphs.