We study the effects of thickness and competition on the equilibria of ride-sharing markets, in which price-setting firms provide platforms to match customers ("riders") and workers ("drivers"). To study thickness, we vary the number of potential workers ("the labor pool") and, to study competition, we change the number of firms from one to two. When the market is sufficiently thick, wage and workers' average welfare decrease with size of the labor pool. Otherwise, wage and workers' average welfare increase with the labor pool, reversing the prediction by the law of demand. Intuitively, workers are "complements" in a thin market --their wage and average welfare goes up with the labor pool-- but they become "substitutes" and compete with each other in a thick market.
We study competition by comparing the monopoly and duopoly equilibria. We find that competition benefits workers: their wage and average welfare are always higher in the duopoly equilibrium. However, the effect of competition on price and customers' average welfare depends on thickness. When the market is not sufficiently thick, there is an adverse effect of competition on customers: price is higher and customers' average welfare is lower in the duopoly equilibrium.
We demonstrate that similar effects apply in other contexts as well. For example, consider improving the matching technology, i.e. improving matching algorithm of the firm so that service quality goes up, given the same labor supply. We show that improving matching technology can be like increasing the labor pool, benefiting workers when the market is not sufficiently thick, while otherwise reducing their wage and average welfare.
This work is an attempt to respond to Wilson Doctrine in procurement auctions. We consider a simple model for procurement problems and solve it to optimality. A buyer with a fixed budget wants to procure, from a set of available workers, a budget feasible subset that maximizes her utility: Any worker has a private reservation price and provides a publicly known utility to the buyer in case of being procured. The buyer's utility function is additive over items. The goal is designing a direct revelation mechanism that solicits workers' reservation prices and decides which workers to recruit and how much to pay them. Moreover, the mechanism has to maximize the buyer's utility without violating her budget constraint. We consider a prior-free setting, i.e. there are no distributional assumptions. Our main contribution is finding the optimal mechanism in this setting, under the "Small Bidders" assumption, which ensures that the bid of each seller is small compared to the buyer's budget.
We generalize the scope of random allocation mechanisms, in which the mechanism first identifies a feasible "expected allocation" and then implements it by randomizing over nearby feasible integer allocations. Previous literature had shown that the cases in which this is possible are sharply limited. We show that if some of the feasibility constraints can be treated as goals rather than hard constraints then, subject to weak conditions that we identify, any expected allocation that satisfies all the constraints and goals can be implemented by randomizing among nearby integer allocations that satisfy all the hard constraints exactly and the goals approximately. By defining ex post utilities as goals, we are able to improve the ex post properties of several classic assignment mechanisms, such as the random serial dictatorship. We use the same approach to prove the existence of ε-competitive equilibrium in large markets with indivisible items and feasibility constraints.
In some developing nations, many end-stage renal disease (ESRD) patients die within weeks of their diagnosis mainly because the costs of kidney transplantation and dialysis are beyond the reach of most citizens. In this paper, we analyze two proposals for extending kidney exchange to include patients in countries in which transplantation is unavailable to them. First, we analyze a recently proposed concept, Global Kidney Exchange, in which a U.S. health authority invites patients with financial restrictions who have willing donors to come to the United States to exchange their donor's kidney with an immunologically incompatible American patient-donor pair and to receive a transplant utilizing the incompatible American donor's kidney for free. We create a dynamic model of this proposal and show that this proposal can be self-financing in the long run. Our analysis shows that, under plausible assumptions, the proposal remains self-financing even when the average dialysis cost of American patients declines below the cost of surgery (as waiting times for transplant are shortened by the increased availability of transplants).
Many school districts apply the student-proposing deferred acceptance algorithm after ties among students are broken exogenously. We compare two common tie-breaking rules: one in which all schools use a single common lottery, and one in which every school uses a separate independent lottery. We identify the balance between supply and demand as the determining factor in this comparison. First we analyze a two-sided matching model with random preferences in over-demanded and under-demanded markets. In a market with a surplus of seats a common lottery is less equitable and there are efficiency trade-offs between the two tie-breaking rules. However, a common lottery is always preferable when there is shortage of seats. The theory suggests that popular schools should use a common lottery to resolve ties. We run numerical experiments with New York City choice data after partitioning the market into popular and non-popular schools. The experiments support our findings.
School districts that implement stable matchings face various decisions that affect students' assignments to schools. We study properties of the rank distribution of students with random preferences when schools use different tie-breaking rules to rank equivalent students. Under a single tie-breaking rule, where all schools use the same ranking, a constant fraction of students are assigned to one of their top choices. In contrast, under a multiple tie-breaking rule, where each school independently ranks students, a vanishing fraction of students are matched to one of their top choices. However, by restricting the students to submitting relatively short preference lists under a multiple tie-breaking rule, a constant fraction of students will be matched with one of their top choices, whereas only a "small" fraction of students will remain unmatched.