Essays on Mechanism Design

This thesis is a collection of three essays on mechanism design. In Chapter 1, we consider a general Informed Principal Problem in the context of procurement. Both the potential suppliers and the buyer hold some private information: each supplier knows his cost of production, the buyer knows how much each supplier's product fits her technical requirements. We derive the optimal auction in this environment, and analyze the implementation problem with special emphasis on three aspects that are particularly relevant in real practice: privacy protection, dynamic consistency, and simplicity. We design a dynamic mechanism, the Modified English Auction, that implements the optimal auction outcome, is privacy preserving, dynamically consistent, and simple. Chapter 2 is a joint work with Joao Leao. How do mechanims like hotwire.com work? What is their economic impact on the existing markets of hotel rooms, airplane tickets, and rental cars? We address these questions by investigating whether lotteries over the basic goods can be profitably used by any of the market participants. We consider lotteries in which the buyers win a prize for sure, but they do not know which one. Our main finding is that the perfect cartel always uses lotteries to maximize its profits. Moreover, under specific conditions, the entry of a lottery provider in a competitive market may bring the existing firms closer to the cartel solution. The introduction of lotteries has two effects. First, the firms can use them to price-discriminate their consumers. Second, the firms can use lotteries to cover a larger part of the market. Indeed, the consumers who find the basic goods too expensive may still want to buy cheaper lottery tickets. In Chapter 3 we initiate the formal analysis of the First Price-First Score Auction in a general context where the auctioneer is a seller and two bidders compete to buy one indivisible good. The auctioneer's preferences are assumed to directly depend on the identity of the buyer to whom the good is allocated. In this auction, the bidders submit monetary bids, and then the seller decides which bid to accept after comparing the bidders' scores. A particular class of auction we focus on have simple scoring functions: each bidder's score is given by the summation of his bid and a bidder-specific additional parameter. Our main goal is to obtain the specification of the problem that generates a closed-form analytical solutions for the bidding strategies. The task is complicated as there are at least two sources of asymmetries inherent to the problem that can quickly lead to intractable formulas. The main contribution of this work is to provide closed formulas for the inverse bidding functions. Our results generalize the comparison of bidding strategies in asymmetric first price auctions obtained by Maskin and Riley (2002). Even if the asymmetry between the bidders is exogenously introduced by the auctioneer, in equilibrium the disadvantaged bidder bids more aggressively. We are also able to determine the ranges of bids that can be submitted by the two bidders. They are actually different, and their extremes depend on the extra-bid