UC San Diego

This dissertation studies the robust design of institutions when the mechanism designerdoes not fully know the environment. In Chapter 1, I construct a novel random double auction as a robust bilateral trading mechanism for a profit-maximizing intermediary who facilitates trade between a buyer and a seller. It works as follows. The intermediary publicly commits to charging a fixed commission fee and randomly drawing a spread from a uniform distribution. Then the buyer submits a bid price and the seller submits an ask price simultaneously. If the difference between the bid price and the ask price is greater than the realized spread, then the asset is transacted at the midpoint price, and each pays the intermediary half of the fixed commission fee. Otherwise, no trade takes place, and no one pays or receives anything. I show that the random double auction is a dominant-strategy mechanism, always guarantees a positive profit, and maximizes the profit guarantee across all dominant-strategy mechanisms. In Chapter 2, I study the single-unit auction design when the seller is assumed to have information only about the marginal distribution of a generic bidder’s valuation, but does not know the correlation structure of the joint distribution of bidders’ valuations. For the two-bidder case, a second-price auction with uniformly distributed random reserve maximizes the worst-case expected revenue across all dominant-strategy mechanisms. For the N -bidder ( N ≥ 3 ) case, a second-price auction with Beta-distributed random reserve is a maxmin mechanism among standard (only a bidder with the highest bid could win the good) dominant-strategy mechanisms. In Chapter 3, I study the auction design of selling multiple goods when the seller only knows the upper bounds of bidders’ values for each good and has no additional distributional information. The designer takes a minimax regret approach. The expected regret from a mechanism given a joint distribution over value profiles and an equilibrium is the difference between the full surplus and the expected revenue. I find that a separate second-price auction with random reserves minimizes her worst-case expected regret across all participation-securing Bayesian mechanisms.