Discrete implementation of the Groves-Ledyard mechanism

When implementing an economic institution in the field or in the laboratory, the participants' action spaces and the institution's outcomes are typically discrete, while our theoretical analysis of the institution often assumes the sets are continuous. Predictions by the continuous model generally turn out to be good approximations to the performance of the discrete implementation. We present an example in which the continuous version has a unique and Pareto efficient equilibrium, but in which the discrete version often has vastly more equilibria, many of them far from efficient. We show that the same phenomenon appears in two experiments investigating the Groves-Ledyard mechanism, and that it may account for the experimental results.