A Cooperative Value for Bayesian Games

Selfish, strategic players may benefit from cooperation, provided they reach agreement. It is therefore important to construct mechanisms that facilitate such cooperation, especially in the case of asymmetric private information. The two major issues are: (1) singling out a fair and efficient outcome among the many individually rational possibilities in a strategic game, and (2) establishing a play protocol under which strategic players may achieve this outcome. The paper presents a general solution for two-person Bayesian games with monetary payoffs, under a strong revealed-payoff assumption. The proposed solution builds upon earlier concepts in game theory. It coincides with the von Neumann minmax value on the class of zero sum games and with the major solution concepts to the Nash Bargaining Problem. Moreover, the solution is based on a simple decomposition of every game into cooperative and competitive components, which is easy to compute.