Essays on market design and auction theory [electronic resource]
Keywords: Management Science and Engineering.

This dissertation consists of three essays on market design and auction theory. In Chapter 1, I introduce new multidimensional auction mechanisms. In many auctions, because of externalities, each bidder has a different maximum willingness to pay in order to beat each specific competitor, which causes the following new problem. When there are three bidders, two bidders might compete against each other unnecessarily and have worse payoffs than if they had lost to the third bidder, i.e., the two bidders have "group winner regret, " which can also lead to inefficiency. While no one-dimensional-bid mechanism is efficient, the Vickrey-Clarke-Groves (VCG) may require losers to pay. This paper introduces a novel mechanism, the "multidimensional second-price" (MSP) auction (and its open ascending version), and characterizes it. MSP is free of a loser's payment, pairwise stable, and has good incentive properties, including no group winner regret. Moreover, the winner cannot win at any different price by any misreport, and a loser cannot be better off winning by any misreport. MSP is strategyproof for a bidder without externalities imposed by others, and it reduces to the second-price auction when there are no externalities. Simulations suggest that MSP outperforms the second-price auction in terms of both revenue and efficiency. In Chapter 2, I study properties of VCG when externalities exist, and introduce shill bidding strategies that weakly dominate truthful bidding. When externalities exist, VCG is efficient, incentive compatible, and individually rational. However, as occurs in package auctions without externalities, VCG outcomes may not be in the core. Moreover, VCG is not pairwise stable. Due to externalities, several additional problems occur. VCG may require losing bidders to pay, which might be undesirable. Also, it might be budget infeasible, and the auctioneer might need to pay the winner a subsidy. The subsidy problem can occur even when all bids are positive. Furthermore, unlike package auctions without externalities, there exists a shill bidding strategy that weakly dominates truthful bidding. In addition, when this shill bidding is used, there is no Nash equilibrium. Each bidder is better off using an infinite number of shills, which eventually makes VCG undefined. In Chapter 3, I study properties of VCG in the advertising auction setting. Even though VCG is incentive compatible (IC) in the advertising auction setting, the actual implementation of VCG in practice is not VCG per se. The main reason is that the price needs to be determined when the billing event happens at the same time as the estimation of click-through rate (CTR) or position discount (PD) is occurring. After all, advertising auctions charge the estimate of externalities. However, even in this "estimated" VCG (eVCG), CTR miscalibration does not ruin IC. Even when PD miscalibration exists, IC still holds with "perfect competition." Regarding efficiency and revenue, both CTR and PD miscalibrations matter. Interestingly, however, the revenue of the auctioneer does not necessarily decrease by underbidding.