Multiple equilibrium problem and non-canonical correlation devices

A correlated equilibrium for a normal form game is a mediator whose recommendations the players find optimal to follow obediently. A (direct) correlation device or a mediator however may face the multiple equilibrium problem as the obedient strategy profile may be dominated by some other Nash equilibrium in the extended game. This paper addresses the question whether it is possible to avoid this problem by considering non-canonical correlation devices. The paper presents three different non-canonical correlation devices (one with and two without a sunspot) to understand this problem for a parametric version of the Chicken game.