The Power of Mediation in an Extended El Farol Game

TL;DR

This paper demonstrates how a mediator can implement the optimal correlated equilibrium in an extended El Farol game with network effects, significantly reducing social costs and revealing unbounded mediation and enforcement values.

Contribution

It provides an exact characterization of Mediation and Enforcement Values for a complex networked game, highlighting the potential for mediators to improve social outcomes.

Findings

Mediation can significantly lower social costs in the extended El Farol game.

Both Mediation Value and Enforcement Value can be unbounded in this setting.

The paper offers rare exact characterizations for games with mixed network effects.

Abstract

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.