Michael Powers, Martin Shubik

Paper #: 14-11-040

Taking the maximum joint payoff of a 2 × 2 matrix game as a measure of potential social welfare, one can compute a simple “value of government” based upon the difference between this maximum payoff and the joint payoff obtained in noncooperative equilibrium. We construct an efficiency loss index (ELI) as the expected value of this difference divided by the maximum joint payoff, and use the ELI to analyze the amount players would be willing to pay government (or some other third-party referee) to coordinate the outcome of the game either by changing its structure or by providing signals/contracts to coordinate behavior. This analysis is applied to random games with both known and unknown opponent payoffs. We also discuss problems associated with index construction and other modeling limitations.