Equilibrium Selection and Stability for the Groves Ledyard Mechanism

In their seminal paper Groves and Ledyard (1976) construct a balanced incentive compatible mechanism that solves the free-rider problem. In subsequent research, Bergstrom, Simon, and Titus (1983) prove that there exist numerous asymmetric equilibria in addition to the symmetric equilibrium. In the present paper we explicitly solve for the additional equilibria and use computational experiments to examine the structure and stability of the set of equilibria of the Groves Ledyard Mechanism. We find that all of the equilibria found by Berstrom, Simon, and Titus are unstable and that for a high level of the punishment parameter these equilibria do not exist. Further we find that there exists an additional boundary equilibrium for each of the equilibria found by Bergstrom, Simon, and Titus. The boundary equilibria are all stable. ∗Departments of Political Science and Economics and Centers for the Study of Complex Systems and Policy Studies University of Michigan, Ann Arbor, MI 48106. †Department of Economics, Fordham University, Bronx, NY 10458.