Coordinating with a "Problem Solver"

A "problem solver" (PS) is an agent who when interacting with other agents does not "put himself in their shoes" but rather chooses a best response to a uniform distribution over all possible configurations consistent with the information he receives about the other agents' moves. We demonstrate the special features of a PS by analyzing a modified coordination game. In the first stage, each of the other participants-who are treated as conventional players-chooses a location. The PS then receives some partial information about their moves and chooses his location. The PS wishes to coordinate with any one of the conventional players and they wish to coordinate with him but not with each other. Equilibria are characterized and shown to have different properties than those of Nash equilibria when the PS is treated as a conventional player.