The Value of Government and the Efficiency of Noncooperative Equilibrium

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. ∗(Corresponding author) Zurich Group Professor of Risk Mathematics, Department of Finance, School of Economics and Management, Tsinghua University, Beijing 100084, China; e-mail: [email protected]; phone: (8610)62795565. †Seymour H. Knox Professor Emeritus of Mathematical Institutional Economics, Cowles Foundation, Department of Economics, and School of Management, Yale University and External Faculty, Santa Fe Institute. ‡The authors would like to thank Yifeng Liu, Xiaoyun Wang, Jordan Chen, and Jane King for their assistance with numerical examples. The first author would like to thank the AXA Research Fund for its financial support. The second author notes that certain of the ideas for this work originated in discussions with several colleagues at the Santa Fe Institute.