Three Essays in Auctions and Contests

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Zhang, Jun
Auctions , Return Policies , Mechanism Design , Contests , All-Pay Auctions , Lottery , Information Revelation
This thesis studies issues in auctions and contests. The seller of an object and the organizer of a contest have many instruments to improve the revenue of the auction or the efficiency of the contest. The three essays in this dissertation shed light on these issues. Chapter 2 investigates how a refund policy affects a buyer's strategic behavior by characterizing the equilibria of a second-price auction with a linear refund policy. I find that a generous refund policy induces buyers to bid aggressively. I also examine the optimal mechanism design problem when buyers only have private initial estimates of their valuations and may privately learn of shocks that affect their valuations later. When all buyers are \emph{ex-ante} symmetric, this optimal selling mechanism can be implemented by a first-price or second-price auction with a refund policy. Chapter 3 investigates how information revelation rules affect the existence and the efficiency of equilibria in two-round elimination contests. I establish that there exists no symmetric separating equilibrium under the full revelation rule and find that the non-existence result is very robust. I then characterize a partially efficient separating equilibrium under the partial revelation rule when players' valuations are uniformly distributed. I finally investigate the no revelation rule and find that it is both most efficient and optimal in maximizing the total efforts from the contestants. Within my framework, more information revelation leads to less efficient outcomes. Chapter 4 analyzes the signaling effect of bidding in a two-round elimination contest. Before the final round, bids in the preliminary round are revealed and act as signals of the contestants' private valuations. Compared to the benchmark model, in which private valuations are revealed automatically before the final round and thus no signaling of bids takes place, I find that strong contestants bluff and weak contestants sandbag. In a separating equilibrium, bids in the preliminary round fully reveal the contestants' private valuations. However, this signaling effect makes the equilibrium bidding strategy in the preliminary round steeper for high valuations and flatter for low valuations compared to the benchmark model.
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