Essays On Market Design And Auctions
Abstract
My thesis consists of three chapters that contribute to redistribution-driven market design and sponsored link auctions.
Chapter 2 and 3 (co-authored with Charles Zheng) study redistribution-driven market design with endogenous buyers and sellers. In Chapter 2, we consider a large market environment with each individual endowed with equal shares of a limited resources and allowed to buy or sell the shares. We characterize the interim (incentive-constrained) Pareto frontier subject to market clearance and budget balance, and find that at most two prices are needed to attain any (interim) Pareto optimum. Under robust conditions of the primitives, the Pareto optimal allocation is unique, and a single price --- without the help of rationing or lump-sum transfer --- implements the optimal allocation. We find which types gain, and which types lose, when the social planner chooses a rationing mechanism over the single-price solution, as well as which type's welfare weight is crucial to the choice. The finding suggests a market-like mechanism to distribute Covid-vaccines optimally among the population that belongs to the same priority group.
In Chapter 3, we study a quasilinear independent private values set-up to allocate a commonly desirable item (the good) and a commonly undesirable item (the bad). We prove a necessary and sufficient condition for all interim Pareto optimal mechanism to allocate the bad with strictly positive probability, despite that not allocating it at all is part of an ex ante incentive efficient mechanism. The condition holds when types near the low end carry sufficiently high welfare densities. Replacing the welfare weight distribution by a second-order stochastically dominated one improves the prospect of the condition. The Kuhn-Tucker method in the literature is inapplicable because when our condition holds, the monotonicity constraint the method sets aside is binding unless the method suffers indeterminacy in admitting a continuum of solutions to the relaxed problem.
Chapter 4 investigates a sponsored link auction game in which consumers search one set of products (block) before the other, and sellers compete in bids to place their product links to the first block. Consumers are assumed to be unaware of the products in the second block when searching in the first block, search in each block optimally according to Weitzman (1979) and update the current best option during the search. I characterize consumers’ shopping outcomes with the block-by-block search behavior. Letting sellers choose product prices and auction bids together, I find the equilibrium of the complete information second price auction with two payment schemes: fixed payment and per-transaction payment. I find auction revenue and consumer surplus are larger under the fixed payment, and seller profits are larger under the per-transaction payment because the latter distorts the winner's pricing strategy. In the case that a social planner runs the platform, I find a consumer optimal positioning of products if sellers commit to prices before the position is allocated.