A general noncentral hypergeometric distribution (with S. Loertscher and P. Taylor), Communications in Statistics – Theory and Methods, 46(9), 2017: 4579–4598 (A previous version is available here)

Approximating the equilibrium quantity traded and welfare in large markets (with K. Borovkov), Stochastic Models, 33(3), 2017, 411–429 (A previous version is available here)

Working Papers (available upon request)

Optimal market thickness and clearing (with S. Loertscher and P. Taylor)

Clearing markets at a lower frequency increases market thickness at the expense of delay. To determine the optimal market clearing policy, we solve a dynamic mechanism design model in which traders arrival stochastically. As the discount factor approaches one, the gains from optimal dynamic market mechanisms relative to instantaneous market clearing go to infinity, while most gains from using a dynamic mechanism are reaped by the simplest dynamic mechanism which clears markets at an optimally chosen frequency. With binary types, efficient incentive compatible trade is possible if storing at least one trade is optimal, in which case the efficient policy can be implemented with budget-balanced posted prices. With a profit maximizing market maker, market thickness is socially excessive, and ad valorem taxes outperform specific taxes.

The distribution of the equilibrium quantity traded (with S. Loertscher and P. Taylor)

We show that in a large family of models the equilibrium quantity traded has a general non-central hypergeometric distribution. This family includes mechanism design models of two-sided markets, k-double auctions, and any standard auction, provided traders’ types are independent and, on each side of the market, identically distributed. Our results exploit the facts that the efficient quantity traded has a non-central hypergeometric distribution and that the equilibrium quantity traded in these models is quasi-Walrasian. That is, it is determined by the intersection of the demand and supply schedules constructed from monotone transformations of values and costs. Asymptotically, the equilibrium quantity traded is normally distributed.

Dynamic market making (with S. Loertscher and P. Taylor)

We study a dynamic extension of the bilateral trade model of Myerson and Satterthwaite (1983). In each period, a buyer-seller pair arrives and agent types are drawn independently from some well-behaved continuous distributions. All agents share a common discounter factor. The market maker faces the tradeoff between the opportunity cost of delayed trade and increased market thickness in later periods. We derive the first-best allocation rule, the second-best allocation rule and the profit-maximizing allocation rule. Approximate implementation using a posted-price mechanism in period one is also considered. We show that these dynamic mechanisms outperform two benchmark static mechanisms.

Work in Progress

Uncontrolled immigration and refugee matching (with D. Delacrétaz)