On the Existence and Stability of Inefficient Boundary Equilibria in the Groves Ledyard Mechanism

In this paper, we characterize all interior and boundary equilibria of the Groves- Ledyard mechanism for a large class of economies and demonstrate their stability or lack thereof. We prove that the mechanism implements large numbers of inefficient and stable boundary equilibria, one for each of the efficient, asymmetric, interior equilibria found by Bergstrom, Simon, and Titus (BST). We show that the symmetric equilibrium is stable, and that its stability rests on two unstable dynamics that combine to create stability. The boundary equilibria, but not the asymmetric interior equilibria, are also stable. We further show that both sets of asymmetric equilibria can fail to exist in the presence of a large punishment parameter or a constraint on messages.