Research

Markets with multiple divisible goods and quasilinear buyers have been studied widely from the perspective of revenue and welfare. In general, it is well-known that envy-free revenue-maximal outcomes can result in lower welfare than competitive equilibrium outcomes. We study the regime in which buyers have quasilinear utilities with budget constraints, and the seller must find prices and an envy-free allocation that maximises revenue or welfare. Our setup mirrors markets such as ad auctions and the arctic product-mix auction proposed for the exchange of financial assets. Our main result is to show that the unique competitive equilibrium prices are also envy-free revenue-maximal. This coincidence of maximal revenue and welfare is surprising, and breaks down even when buyers have piecewise-linear valuations. In our result, we present a novel characterisation of the set of ‘feasible’ prices at which demand does not exceed supply, show that this set has an elementwise-minimal price vector, and demonstrate that these prices maximise revenue and welfare. The proof also implies an algorithm for finding this unique price vector.

In an epidemic, how should an organization with limited testing resources safely return to in-person activities after a period of lockdown? We study this question in a setting where the population at hand is heterogeneous in both utility for in-person activities and probability of infection. In such a period of re-integration, tests can be used as a certificate of non-infection, whereby those in negative tests are permitted to return to in-person activities for a designated amount of time. Under the assumption that samples can be pooled, the question of how to allocate a limited testing budget in the population to maximize the aggregate utility (i.e.~welfare) of negatively-tested individuals who return to in-person activities is non-trivial, with a large space of potential testing allocations. We show that non-overlapping testing allocations, which are both conceptually and (crucially) logistically more simple to implement, are approximately optimal, and we design an efficient greedy algorithm for finding non-overlapping testing allocations with approximately optimal welfare. In computational experiments, we highlight the efficacy and viability of our greedy algorithm in practice. To the best of our knowledge, we are also first to implement and provide causal evidence on the benefits of utility-weighted pooled testing in a real-world setting. Our pilot study at a higher education research institute in Mexico demonstrates - surprisingly - no worse performance and mental health outcomes of participants in our testing regime than the first-best counterfactual of full reopening without testing.

We study how pricing affects the division of surplus among buyers in auctions for multiple units. Our equity objective may be important, e.g., for competition concerns in downstream markets, complementing the long-standing debate on revenue and efficiency. We study a canonical model of auctions for multiple indivisible units with unit demand buyers and valuations with a private and a common component and consider all pricing rules that are a mixture (i.e., a convex combination) of pay-as-bid and uniform pricing. We propose the winners' empirical variance (WEV), the expected empirical variance of surplus among the winners, as a metric for surplus equity. We show that, for a range of private-common value proportions, a strictly interior mix of pay-as-bid and uniform pricing minimizes WEV. From an equity perspective, auctions with a higher private value component benefit from more price discrimination, whereas only auctions with a sufficiently high common value justify a more uniform pricing rule. We provide a criterion under which strictly mixed pricing dominates uniform pricing, a partial ranking of different mixed pricing formats, and bounds on the WEV-minimizing pricing under the assumption of log-concave signal distributions. In numerical experiments, we further illustrate the WEV-minimal pricing as a function of the private-common-value mix.

I consider a package assignment problem where multiple units of indivisible objects are allocated to individuals. The seller can specify additional costs or cost savings on certain packages of objects: e.g., a manufacturer may incur cost savings if they obtain a range of products or services from a single supplier. The objective is to find a socially efficient allocation among buyers. I propose a sealed-bid auction with a novel cost function graph to express the seller's preferences. The graph structure facilitates the use of linear programming to find anonymous, competitive, and package-linear prices. If agents act as price takers, these prices support a Walrasian equilibrium, and I provide additional conditions under which an equilibrium always exists. The auction design guarantees fairness and transparency in pricing, and it admits preferences of the seller or auctioneer over the type and degree of concentration in the market.

I study strategic bidding behaviour in three pay-as-bid multi-object auctions: a Product-Mix auction, a sequential auction, and a simultaneous auction. In a theoretical model, bidders are assumed to behave optimally, i.e. are maximising their expected surplus. This model predicts that, in equilibrium, the Product-Mix and the sequential format perform nearly identically with respect to bidder surplus, revenue, and welfare. The simultaneous auction performs only slightly worse than the other two formats. I test if the equivalences hold up in a virtual lab experiment. I consider a bidding environment identical to the theoretical model of an asymmetric market, but also study a bidding environment with symmetric bidders, a more general setting for which current Bayes-Nash equilibrium models cannot make predictions. The empirical results are mostly in stark contrast with predictions of the theory: the Product-Mix auction outperforms both other formats in bidder surplus and welfare, while the simultaneous auction generates the highest revenue. In the market with symmetric bidders, these results are much more pronounced: payoffs in the PMA are 90% (156%) higher than in the sequential (simultaneous) auction, and efficiency is 12% higher.

I study equilibria in Product-Mix, sequential, and simultaneous auctions, which are used to sell differentiated, indivisible goods. A flexible bidder with unit demand, interested in buying any of the goods, competes against several inflexible bidders, each interested in only one specific good. For first-price and second-price payments, I obtain theoretical results on equilibrium bidding, and compare efficiency, revenue, and bidder surplus numerically. Differences in outcomes between Product-Mix and sequential auctions are small for a range of value distributions. The simultaneous auction performs worst in all dimensions, and differences in performance vary substantially with the degree of competition the flexible bidder faces.