Articles SOME LIMITATIONS OF THE GROVES-LEDYARD OPTIMAL MECHANISM Joseph Greenberg, Robert Mackay,, and Nicolaus Tideman Although the Groves-Ledyard Optimal Mechanism (Groves and Ledyard, this volume) satisfies the Nash Equilibrium, the Lindahl-Samuelson, and the Budget Balance conditions, it suffers from at least two important limitations. These limitations arise from the Optimal Mechanlsm's failure to satisfy the Dominant Equilibrium Condition. Since a dominant strategy equilibrium does not exist for the Optimal Mechanism, the best message for a consumer depends upon summary statistics from the messages of all other consumers. Therefore, it is important to address the question of how the Nash equilibrium is to be attained. Some adjustment or solution process is required. In fact, without an explicityly specified adjustment process it is difficult to conceive of the Optimal Mechanism as being, in any meaningful sense, a solution to the Free Rider Problem. Groves and Ledyard do not suggest an adjustment process nor do they consider the problms raised for the Optimal Mechanism by the necessity of an adjustment process. Once the need for an adjustment process is recognized, two difficulties are apparent. First, with an adjustment process one must question the appropriateness of the Groves and Ledyard assumption that consumers behave competitively, treating the messages sent to the government by other agents as fixed parameters. *Center for Operation Research and Econometrics, Heverlee, Belgium and Virginia Polytechnic Institute and State University, Tulane University, Virginia Polytechnic Institute and State University,respectively. The authors would like to thank Steven Salop for helpful comments and John Ledyard for pointing out a mathematical error in an earlier draft of this paper.