Cooperative congestion games: existence of a Nash-stable coalition structure
This paper studies a model for cooperative congestion games. There is an array of cooperative games V and a player’s strategy is to choose a subset of the set V. The player gets a certain payoff from each chosen game. The paper demonstrates that if a payoff is the Shapley or the Banzhaf value, then the corresponding cooperative congestion game has a Nash equilibrium in pure strategies. The case is examined where each game in V has a coalition partition. The stability of the vector of coalition structures is determined, taking into account the transitions of players within a game and their migrations to other games. The potential function is defined for coalition partitions, and is used as a means of proving the existence of a stable vector of coalition structures for a certain class of cooperative game values.