Belief Extraction in Mechanism Design

Abstract

In many settings, the designer of an institution is less informed about the economy than are the agents who will ultimately participate in that institution. This dissertation explores how such an uninformed designer can learn features of the economy that are common knowledge among the agents and use the extracted information to design better institutions.

Chapters 1 and 2 study how an uninformed seller can induce potential buyers to reveal the revenue maximizing reservation price for an auction. Chapter 1 explores mechanisms in which a seller runs a sealed-bid second-price auction and simultaneously surveys the buyers' beliefs about others' valuations. The seller offers bets that incentivize truthful reporting of beliefs, and for a general class of

environments, truth-telling is the unique equilibrium. Losing bidders' reports are used to set an interim optimal reserve price for the winner. As a result, these mechanisms guarantee the seller an optimal worst-case revenue-share of the efficient surplus.

Chapter 2 considers sealed-bid second-price auctions in which instead of reporting beliefs, each bidder recommends a reservation price to be used when they lose the auction. If the recommendation is used, the bidder is rewarded with a small share of revenue. Revenue sharing aligns the incentives of the seller and losing buyers, but creates an incentive to "throw" the auction when a buyer expects to win at a price close to his valuation. When the distribution of valuations satisfies a monotone hazard rate assumption, the mechanism has a symmetric and monotonic equilibrium. As the bidders' revenue shares go to zero, bid shading disappears and the equilibrium results in optimal reserve prices.

Chapter 3 explores general mechanisms that a designer can use to

extract common knowledge for the purpose of building that information into a mechanism. For private-good environments such as those considered in Chapters 1 and 2, mechanisms are constructed that allow the designer to recover the agents' common knowledge at arbitrarily small cost to any ultimate mechanism design goals.