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

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 + √ 3/3 = 1.577. We also consider the price of anarchy of correlated equilibria. We extend some of the results in [2, 4] to correlated equilibria and show that for the sum social cost, the price of anarchy is 2.5. The same bound holds for symmetric games as well. This matches the lower bounds given in [2, 4] for pure Nash equilibria. We also extend the results in [2] for weighted congestion games to correlated equilibria. Specifically, we show that when the social cost is the total latency, the price of anarchy is (3 + √ 5)/2 = 2.618.