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A mediator implements a correlated equilibrium when it proposes a strategy toeach player confidentially such that the mediator's proposal is the bestinterest for every player to follow. In this paper, we present a mediator thatimplements the best correlated equilibrium for an extended El Farol game withsymmetric players. The extended El Farol game we consider incorporates bothnegative and positive network effects.  We study the degree to which this type of mediator can decrease the overallsocial cost. In particular, we give an exact characterization of MediationValue (MV) and Enforcement Value (EV) for this game. MV is the ratio of theminimum social cost over all Nash equilibria to the minimum social cost overall mediators, and EV is the ratio of the minimum social cost over allmediators to the optimal social cost. This sort of exact characterization isuncommon for games with both kinds of network effects. An interesting outcomeof our results is that both the MV and EV values can be unbounded for our game.

The Power of Mediation in an Extended El Farol Game