Mathematica Pannonica 18/2 (2007), 205–217 FINITE NEIGHBORHOOD GAMES WITH BINARY CHOICES Ugo Merlone Statistics and Applied Mathematics Department, University of Torino, Piazza Arbarello 8, Torino I-10122, Italy Ferenc Szidarovszky Systems and Industrial Engineering Department, The University of Arizona, Tucson, Arizona 85721-0020, USA Miklos N. Szilagyi Electrical and Computer Engineering Department, The University of Arizona, Tucson, Arizona 85721-0104, USA Dedicated to Professor Maurer on the occasion of his 80 th birthday Received : February 2007 MSC 2000 : 91 A 20, 91 A 50, 91 A 70 Keywords : Finite neighborhood games, equivalence classes, canonical forms. Abstract: Finite neighborhood repeated games with large number of players are examined. Each agent has the choice between two actions and its payoff depends on the number of other players with the same choice. We first showed that the number of different types of games is finite and then we derived tight upper bounds for the number of game types in the general case and also with monotonic and linear payoff functions. The different game types are identified by equivalence classes generated by canonical forms, and in the linear case a system of linear inequalities is derived that characterizes all games being equivalent to any given game. Numerical examples illustrate the theoretical results. Both bounded and unbounded examples are shown.