Counting Groves-Ledyard Equilibria Via Degree Theory

Ted Bergstrom, University of California, Santa Barbara
Carl Simon, University of Michigan
Charles Titus, University of Michigan

Abstract

A Nash equilibria of the Groves-Ledyard mechanism is Pareto optimal. But this may not be much use if there are many distinct Nash equilibria, since it is not clear that the mechanism would converge on any one of them. This paper shows that if preferences are quasi-linear, the Groves-Ledyard mechanism has a unique Nash equilibrium, but even in the simplest class of preferences in which demands for public goods are affected by incomes, the number of equilibria increases exponentially with the number of consumers. The paper makes use of some pretty mathematics and even sports a drawing of Whitney's umbrella.