Computer Science – Computer Science and Game Theory
Scientific paper
2012-03-26
Computer Science
Computer Science and Game Theory
21 pages, 2 figures
Scientific paper
This work shows that the formation of a finite number of coalitions in a nonatomic network congestion game benefits everyone. At the equilibrium of the composite game played by coalitions and individuals, the average payoff to each coalition and the individuals' (common) payoff are all higher than in the corresponding nonatomic game (without coalitions). The individuals' payoff is higher than the average payoff to any coalition. Similarly, the average payoff to a coalition is higher than that to any larger coalition. Whenever some members of a coalition become individuals, the individuals' cost is increased. In the case of unique coalition, both the average cost to the coalition and the individuals' payoff increase with the size of the coalition. If in a sequence of composite games a finite number of coalitions are fixed while the size of the remaining coalitions goes to zero, the equilibrium of these games converges to the equilibrium of a composite game played by the same fixed coalitions and the remaining individuals.
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