Congestion games (CG) are a class of games in game theory. They represent situations which commonly occur in roads, communication networks, oligopoly markets and natural habitats. There is a set of resources (e.g. roads or communication links); there are several players who need resources (e.g. drivers or network users); each player chooses a subset of these resources (e.g. a path in the network); the delay in each resource is determined by the number of players choosing a subset that contains this resource. The cost of each player is the sum of delays among all resources he chooses. Naturally, each player wants to minimize his own delay; however, each player's choices impose a negative externality on the other players, which may lead to inefficient outcomes.
The research of congestion games was initiated by the American economist Robert W. Rosenthal in 1973.[1] He proved that every congestion game has a Nash equilibrium in pure strategies (aka pure Nash equilibrium, PNE). During the proof, he in fact proved that every congestion game is an exact potential game. Later, Monderer and Shapley[2] proved a converse result: any game with an exact potential function is equivalent to some congestion game. Later research focused on questions such as:
Does the existence of equilibrium, as well as the existence of a potential function, extend to more general models of congestion games?
What is the quantitative inefficiency of congestion games?
What is the computational complexity of finding an equilibrium?
^Rosenthal, Robert W. (1973), "A class of games possessing pure-strategy Nash equilibria", International Journal of Game Theory, 2: 65–67, doi:10.1007/BF01737559, MR 0319584, S2CID 121904640.
^Monderer, Dov; Shapley, Lloyd S. (1996-05-01). "Potential Games". Games and Economic Behavior. 14 (1): 124–143. doi:10.1006/game.1996.0044. ISSN 0899-8256.
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