Non-Excludable Dynamic Mechanism Design
28 Pages Posted: 17 Dec 2020
Date Written: October 21, 2020
Dynamic mechanism design expands the scope of allocations that can be implemented and the performance that can be attained compared to static mechanisms. Even under stringent participation constraints and restrictions on transfers, recent work demonstrated that it is possible for a designer to extract the surplus of all players as revenue when players have quasilinear utilities and the number of interactions is large. Much of the analysis has focused on excludable environments (i.e., any player can be excluded from trade without affecting the utilities of others). The mechanisms presented in the literature, however, do not extend to non-excludable environments. Two prototypical examples of such environments are: (i) public projects, where all players must have the same allocation; and (ii) non-disposable goods, where each item must be allocated to some player. We show a general mechanism that can asymptotically extract full surplus as revenue in such environments. Moreover, we provide a tight characterization for general environments, and identify necessary and sufficient conditions on the possibility of asymptotic full surplus extraction. Our characterization is based on the geometry of achievable utility sets -- convex sets that delineate the expected utilities that can be implemented by static mechanisms. Our results provide a reduction from dynamic to static mechanism design: the geometry of the achievable utility set of static mechanisms completely determines whether it is possible to fully extract surplus in the limit.
Keywords: dynamic mechanism design, non-excludability, geometric method
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