Congestion games revisited

Strategic games are considered where the players derive their utilities from participation in certain “processes”. Two subclasses consisting exclusively of potential games are singled out. In the first, players choose where to participate, but there is a unique way of participation, the same for all players. In the second, the participation structure is fixed, but each player may have an arbitrary set of strategies. In both cases, the players sum up the intermediate utilities; thus the first class essentially coincides with that of congestion games. The necessity of additivity in each case is proven. Financial support from Presidential Grants for the State Support of the Leading Scientific Schools (NSh-1843.2003.01 and NSh-5379.2006.1), the Russian Foundation for Basic Research (grant 05-01-00942), the Spanish Ministry of Education (project SEJ2004-00968), and the Lady Davis Foundation (a fellowship at the Technion, Haifa) is acknowledged. I thank Francisco Marhuenda and Dov Monderer, respectively, for procuring the last two grants. My deepest gratitude and apology are due to an anonymous referee, who carefully read two versions of the paper, suggested several improvements, and uncovered several errors, including a wrong formulation of Theorem 1. Finally, I apologize to Mikhail Gorelov, who had warned me that something was wrong with the theorem (unfortunately, I failed to pay proper attention).