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