On the price of mediation

We study the relationship between the social cost of correlated equilibria and the social cost of Nash equilibria. In contrast to previous work focusing on the possible benefits of a benevolent mediator, we define and bound the Price of Mediation (PoM): the ratio of the cost of the worst correlated equilibrium to the cost of the worst Nash. We observe that in practice, the heuristics used for mediation are frequently non-optimal, and from an economic perspective mediators may be inept or self-interested. Recent results on computation of equilibria also motivate our work. We consider the Price of Mediation for general games with small numbers of players and pure strategies. For games with two players each having two pure strategies we prove a tight bound of two on the PoM. For larger games (either more players, or more pure strategies per player, or both) we show that the PoM can be unbounded. Most of our results focus on symmetric congestion games (also known as load balancing games). We show that for general convex cost functions, the PoM can grow exponentially in the number of players. We prove that PoM is one for linear costs and at most a small constant (but can be larger than one) for concave costs. For polynomial cost functions, we prove bounds on the PoM which are exponential in the degree.