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This dissertation studies two elements of auction design that are important to understand environments where multiple auctioneers compete against each other: heterogeneity in bidders' preferences, and endogenous information structures. The first research chapter studies a model of competing auctions in which bidders have heterogeneous preferences. I provide a novel characterization of the set of participation rules and show that contrary to results in models with homogeneous goods, bidders' selection of trading partners is non random. I also show that changes in reserve prices affect not only the distribution of valuations of participants but also the probability with which every bidder visits the auctions. This introduces a novel trade-off between screening and traffic effect not present in models with homogeneous goods. The second research chapter examines a model of competing auctions in which sellers can release information that allows bidders to learn their valuations before choosing trading partners. I provide a set of sufficient conditions for the existence of a unique equilibrium in which both sellers supply information. These conditions involve restrictions on the prior distribution of bidders valuations. The existence of this equilibrium is independent of the number of bidders, which differs considerably from results in models with a single auctioneer where releasing information is optimal for the auctioneer only if the number of bidders is sufficiently large. The last chapter re-examines the problem of information provision in competing auctions in a framework where sellers can also post reserve prices. The inclusion of reserve prices makes the existence of an equilibrium in which both sellers do not supply information less likely because sellers can use reserve prices to appropriate of some of the surplus generated by information provision. I show the existence of a threshold number of bidders such that the information provision game admits a unique equilibrium in which both sellers release information provided that the actual number of bidders is above this threshold.
In three directed search models with horizontal differentiation, this thesis characterizes the unique symmetric equilibrium for each model and studies the welfare property of equilibrium allocations. In Chapter 2, horizontal differentiation is modeled as buyers' valuations being independent. In equilibrium, sellers use a mixed strategy with the support consisting of a countable number of prices. Equilibrium price dispersion exists and equilibrium allocation is constrained inefficient due to price dispersion. Chapter 3 extends the model in Chapter 2 by allowing different degrees of horizontal differentiation. With large degrees of horizontal differentiation, sellers use a mixed strategy qualitatively similar to the equilibrium in Chapter 2. With small degrees of differentiation, sellers use a pure strategy. Chapter 4 extends the model in Chapter 2 by allowing differentiation to be endogenous. Initially buyers are equally uncertain about the characteristics of sellers' goods and no differentiation exists. Then sellers choose prices together with the amounts of information disclosed to buyers about the characteristics of sellers' goods. Information disclosure leads to differentiation after buyers receive the information. It is shown that a seller's profit by disclosing full information is higher than that by disclosing partial information. In equilibrium both sellers disclose full information and use a pricing strategy that is identical to the equilibrium in Chapter 2.
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