Conferences at Department of Economics, University of Toronto, Canadian Economic Theory Conference 2016

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Unobserved Mechanisms

Michael Peters*, Hao Li

Date: 2016-05-08 10:15 am – 10:45 am
Last modified: 2016-04-15

Abstract


/* Layout-provided Styles */ div.abstract { font-size: small; margin-top: 0.7ex; margin-bottom: 0.7ex; margin-left: 3ex; margin-right: 3ex; text-align: left; } span.abstract_label { font-style: normal; font-variant: small-caps; font-size: small; } Abstract. A fundamental assumption of mechanism design is that agents are fully aware of commitments that are made by principals, and that they believe that these commitments will be carried out. There is a considerable literature devoted to analyzing what happens when principals can't commit. However, a more relevant consideration for the kinds of mechanism that are used in on line markets is that sellers' can commit, but that not all buyers can observe and understand what these commitments are. In this sense, mechanism design becomes a game with imperfect information in which some agents cannot distinguish different mechanisms offered by principals. Mechanism designers then face a trade off between the surplus they can extract from informed agents by using commitments, and the surplus they can extract from uninformed buyers from exploiting their ignorance. For instance, a second price auction that is revenue maximizing with complete commitment may not constitute and equilibrium for a game of mechanism design. In an auction, the seller commits to a mechanism that makes a price offer to one of the buyers that is contingent on bids he receives. If some buyers do not understand how the bids are being used, the seller might want to deviate from a second price auction to something that looks more like a first price auction in order to extract more surplus from the uninformed bidders. In this preliminary version of the paper, we consider a two value auction and show that if the probability with which each bidder is uninformed about the mechanism the seller is using is very low, then the standard optimal auction constitutes an equilibrium in the sense that them mechanism designer has no incentive to deviate to any alternative mechanism. We also characterize the equilibrium mechanism in the case where buyers are more likely to be uninformed. In this case, the sellers' best mechanism has the property that high value uninformed bidders send randomized messages. These messages are designed to make deviations by the seller unprofitable. They have the unfortunate side effect that the resulting equilibrium cannot be ex post efficient. We also explore the case with a continuum of types. We show that sellers can design mechanisms with extended messages that allow informed bidders to reveal that they are informed to the seller. The seller can then offer them standard mechanisms with an added incentive constraint - all informed bidders prefer to reveal that they are informed (uninformed bidders cannot pretend to be informed in this mechanism). We give a partial characterization of the equilibrium mechanism for this case, and show that it cannot be ex post efficient.

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