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Mechanism Design With Aftermarkets: Cutoff Mechanisms
Author(s) -
Dworczak Piotr
Publication year - 2020
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta15768
Subject(s) - cutoff , generality , mechanism design , mechanism (biology) , computer science , outcome (game theory) , realization (probability) , object (grammar) , class (philosophy) , mathematical optimization , mathematical economics , artificial intelligence , economics , mathematics , statistics , philosophy , physics , management , epistemology , quantum mechanics
I study a mechanism design problem in which a designer allocates a single good to one of several agents, and the mechanism is followed by an aftermarket —a post‐mechanism game played between the agent who acquired the good and third‐party market participants. The designer has preferences over final outcomes, but she cannot design the aftermarket. However, she can influence its information structure by publicly disclosing information elicited from the agents by the mechanism. I introduce a class of allocation and disclosure rules, called cutoff rules , that disclose information about the buyer's type only by revealing information about the realization of a random threshold (cutoff) that she had to outbid to win the object. When there is a single agent in the mechanism, I show that the optimal cutoff mechanism offers full privacy to the agent. In contrast, when there are multiple agents, the optimal cutoff mechanism may disclose information about the winner's type; I provide sufficient conditions for optimality of simple designs. I also characterize aftermarkets for which restricting attention to cutoff mechanisms is without loss of generality in a subclass of all feasible mechanisms satisfying additional conditions.