Robust Mechanism Design

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An important recent application of economic theory has been to the design of markets. For example, the design of the spectrum auctions in the United States and around the world has been much influenced by recent developments in auction theory and the theory of mechanism design. However, much of the theory has been developed with a simplified view of (1) how different market participants value the objects for sale; and (2) what they believe other market participants' beliefs. Such simplifying assumptions have been made for the sake of tractability and the resulting theories have been highly successful. However, one concern of practitioners and theorists alike has been that the "optimal" mechanisms derived from theory are sometimes too complex to be implemented in practice, which has lead for a search for simpler mechanisms that seem to be more robust to the underlying description of the environment. Our project will use new developments in game theory, allowing for richer "types" of market participants (including richer beliefs) to provide a theoretical justification for the use of simple mechanisms.The project addresses two separate but linked objectives. First, we examine how robust received mechanisms are to allowing the richer type spaces. In particular, researchers often argue that solution concepts stronger than Bayes-Nash equilibrium, such as dominance solvability and ex post equilibrium, are desirable because they are "robust," although the exact notion of robustness is not always described. One way of formalizing robustness is to examine whether results continue to hold on richer type spaces. In our proposal, we discuss various type spaces in between the naive type space and the universal type space, and examine how different mechanisms' performances vary as we vary the type space.Our second objective is to develop new optimal mechanisms for particular type spaces, intermediate between the standard space of all payoff-relevant types and the universal type space. Optimality in this context refers to the objective of the mechanism designer, which may coincide with social efficiency or simply be a revenue maximization problem for the designer. When the objective of the mechanism designer requires him to maximize an expected value, it will be appropriate to consider subspaces of the universal type space, which can be generated from a prior distribution function.