On the Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games,,

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Abstract

We consider the price of stability for Nash and correlated equilibria of linear congestion games. The price of stability is the optimistic price of anarchy, the ratio of the cost of the best Nash or correlated equilibrium over the social optimum. We show that for the sum social cost, which corresponds to the average cost of the players, every linear congestion game has Nash and correlated price of stability at most 1.6. We also give an almost matching lower bound of \(1+\sqrt{3}/3=1.577\) .

We also consider the price of anarchy of correlated equilibria. We extend existing results about Nash equilibria to correlated equilibria and show that for the sum social cost, the price of anarchy is exactly 2.5, the same for pure and mixed Nash and for correlated equilibria. The same bound holds for symmetric games as well. We also extend the results about Nash equilibria to correlated equilibria for weighted congestion games and we show that when the social cost is the total latency, the price of anarchy is \((3+\sqrt{5})/2=2.618\) .

Research supported in part by the IST (FLAGS, IST-2001-33116) programme.
Research supported in part by the programme EΠEAEK II under the task “ΠYΘAΓOPAΣ-II: ENIΣXYΣH EPEYNHTIKΩN OMAΔΩN ΣTA ΠANEΠIΣTHMIA (project title: Algorithms and Complexity in Network Theory)” which is funded by the European Social Fund (75%) and the Greek Ministry of Education (25%).
Research supported in part by the programme ΠENEΔ 2003 of General Secretariat for Research and Technology (project title: Optimization Problems in Networks).