A universal construction generating potential games

Strategic games are considered where each player's total utility is the sum of local utilities obtained from the use of certain “facilities.” All players using a facility obtain the same utility therefrom, which may depend on the identities of users and on their behavior. If a “trimness” condition is satisfied by every facility, then the game admits an exact potential; conversely, if a facility is not trim, adding it to a potential game may destroy that property. In both congestion games and games with structured utilities, all facilities are trim. Under additional assumptions the potential attains its maximum, which is a Nash equilibrium of the game.