Comment on “ Thirteen Reasons Why the Vickrey - Clarke - Groves Process is Not Practical ” by Michael Rothkopf

Whenever a research topic which has developed in one field spreads to new disciplines, there is the potential benefit of new perspectives and new tools opening unexplored avenues, and there is the potential danger of re-learning the old lessons of the originating discipline. The spread of auction theory and, more generally, mechanism design to computer science, operations research, and related fields is certainly no exception. On one hand, important practical issues such as the computability of equilibria have long been ignored by the economics profession. On the other hand, computer scientists and operations researchers have focused almost exclusively on the dominant strategy mechanisms developed in the 1970s with no attention to the vast and elegant implementation literature of the 1980s and 1990s, much of which was developed with the focus of finding continually better mechanisms. Fortunately, cross-disciplinary discussions such as this can help both sides reap the benefits of progress without incurring the costs of repetition. My hope is that Michael Rothkopf’s critique of the VCG mechanism will lead non-economists interested in mechanism design to explore the implementation literature and to use new tools to generate additional useful insights. Much of the renewed interest in mechanism design has focused narrowly on auction design, which is certainly due to the simultaneous rise in online auction participation and in research on e-commerce platforms. Similarly, Rothkopf’s critiques are aimed only at the VCG mechanism’s use in auction environments. The more general definition of the VCG mechanism, however, extends to a very broad class of social choice and allocation problems. Unfortunately, the impossibility results obtained in the more general environments imply that the VCG mechanism is necessarily inefficient; and it is this inefficiency, among other concerns, that led to the development of the implementation literature. Hopefully non-economists, seeing related deficiencies in dominant strategy mechanisms, will continue to follow this path. The following describes the fundamental difficulty with the VCG mechanism. Suppose we want a mechanism for some very general setting, and we want our agents always to have a dominant strategy that results in a Pareto optimal outcome. Immediately we are faced with the impossibility results of Gibbard (1973) and Satterthwaite (1975), which tells us that if every possible preference is admissible, and if the mechanism must always have a dominant strategy, then the outcomes that must be chosen must be exactly those chosen by simply assigning one agent to be a dictator. The easiest escape from this dead-end is to get rid of the assumption that every possible preference is admissible. For example, we could proceed by assuming agents’ preferences are of the quasilinear form vi (y) +mi where y is the allocation decision and mi represents holdings of some numeraire