Topics in Implementation Theory and Mechanism Design

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This project contributes to implementation theory, one of the most important areas in the last ten years of economic theory. Implementation theory tells us in very general terms what can and cannot be accomplished through incentive contracts. This project pursues three directions: mechanism design in dynamic or repeated environments, application of general results of implementation theory to specific economic settings, and theoretical modelling of processes by which agents choose a mechanism. The first part extends the basic model of full implementation to dynamic settings, i.e., settings in which allocations and payoffs occur over a sequence of periods. The second part applies implementation theory to problems of public goods provision, bargaining, and auctions. The third part explores the question of how mechanisms are selected. In particular, if the decision of which mechanism to play is made by the players themselves at the interim stage, then the actual process of selecting the mechanism may reveal information. The project studies the effects of this information transmission on mechanism choice. It applies this to the study of how cartels of diverse firms share information and collude. Advances in implementation theory are important because this theory provides analysts with powerful analytical tools for studying institutional design. The early work in this field resulted in general impossibility theorems, proofs that certain basic societal goals could not be reconciled and that trade-offs were necessary. Recent work by the investigators and others have obtained remarkable results about what can be accomplished by changes in economic institutions. By extending these models to a dynamic setting, the investigators will be able to rigorously study the economic implications of the evolution of institutions over time.