The power of mediation in an extended El Farol game

Dieter Mitsche (1) , George Saad (2) , Jared Saia (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 UNM Computer Science department [New Mexico]

A mediator implements a correlated equilibrium when it pro- poses a strategy to each player con dentially 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 e ffects. 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 of this type, and EV is the ratio of the minimum social cost over all mediators of this type to the optimal social cost. This sort of exact characterization is uncommon for games with both kinds of network e ffects. An interesting outcome of our results is that both the MV and EV values can be unbounded for our game.

Domaines: Informatique et théorie des jeux [cs.GT]

Dieter Mitsche, George Saad, Jared Saia. The power of mediation in an extended El Farol game. Symposium on Algorithmic Game Theory 2013, Oct 2013, Aachen, Germany. ⟨hal-00923117⟩