The Existence and Stability of Equilibria in the Groves Ledyard Mechanism

In this paper, we describe all interior and boundary equilibria of the GrovesLedyard mechanism and test their stability. We provide closed form solutions for the equilibria discovered by Bergstrom, Simon, and Titus and show that these equilibria fail to exist when the punishment parameter is high. We further show that the Groves-Ledyard equilibrium is the unique stable interior equilibrium for all values of the punishment parameter. Interestingly, this stability rests on two dynamics each of which is unstable. We also show that all of the equilibria found by Bergstrom, Simon, and Titus are unstable. Finally, we locate an additional set of boundary equilibria of the same cardinality as the Bergstrom Simon and Titus equilibria and show that these are inefficient and stable. Yet, they also only exist for low values of the punishment parameter.