We consider combinatorial exchanges where agents have (possibly random) endowments and ordinal preferences over bundles of indivisible goods. We focus on the ordinal core—the set of all individually rational lottery assignments which cannot be blocked by a coalition whose members trade probability shares and receive first-order stochastically dominating lotteries. We show that the ordinal core is always non-empty and that any ordinal core allocation can be implemented as a lottery over near-feasible and ex-post efficient outcomes. In fact, we prove that there is always a set of allocations in the core, which we call the competitive core, that can be supported by prices arising from a novel competitive equilibrium foundation. When endowments are deterministic, competitive core allocations can be implemented over near-feasible ex-post core outcomes. Moreover, competitive core allocations are ordinally envy-free and ex-post envy-free up to one good (where envy is only justified if another agent’s endowment is either smaller or worth less in equilibrium). A mechanism that selects a competitive core allocation is strategyproof in the large. Our framework can be used in many real-world market design applications, such as organ exchanges, tuition exchanges, time bank sharing, shift exchanges, and resource reallocation.

In today's financial landscape, traditional exchanges compete against online trading platforms. A critical point of competition centers around transaction costs. While traditional exchanges adhere to transparent transaction costs, many online trading platforms, under the guise of `zero-commission trading', conceal their transaction costs. In this paper, I show that hidden transaction costs induce additional volatility in the form of price cycles in markets that would be stable if transparent transaction costs were charged. To compete with the profit opportunities from price cycles, platforms with transparent costs must reduce them below the optimal monopolist level to attract traders. In this duopoly, I show that there is a market equilibrium: more risk-averse traders prefer transparent transaction costs, while less risk-averse traders choose hidden costs. Depending on the risk attitudes of traders, transparent transaction costs can be more or less efficient than hidden transaction costs. Finally, I show that hidden transaction costs can potentially lead to market failure, as forward-looking and patient traders may exploit price cycles through strategically placing more aggressive orders.

Transaction costs are ubiquitous in markets. We show that they can fundamentally alter incentives and welfare. We categorize transaction costs into two types. Uniform transaction costs --- such as fixed and price fees --- incur unavoidable dead-weight loss but preserve key asymptotic properties of markets without transaction cost. Discriminatory transaction costs --- such as spread fees --- can avoid dead-weight loss but asymptotically lead to complex strategic behavior that may result in market failure. We show how optimal design depends on market size and traders' beliefs: uniform fees are often optimal in large markets, while discriminatory fees may be preferable in small markets. 

Double auctions are amongst the most widespread market mechanisms that clear demand and supply in two-sided markets. Major stock exchanges, for example, use double auctions to open and close every day. Despite their ubiquity, there is a disconnect between practice and theory, and there is a lack of a general framework to study them. In this paper, we provide the first unified definition of double auctions that applies to both finite and infinite markets, is well-behaved in the limit, and nests relevant pre-existent implementations. In contrast to prior work, our definition does not rely on any regularity assumptions, and allows ties and gaps in reported values, two phenomena naturally occurring in important markets. We show that our Double Auction is the unique feasible mechanism that implements a core-stable outcome, and also the unique mechanism that implements Walrasian equilibrium. We provide further axiomatizations to pin down focal pricing rules used in theory and practice. Finally, we provide necessary and sufficient conditions on traders' beliefs for our Double Auction to be asymptotically incentive-compatible, proving, in particular, that our Double Auction is Strategy-Proof in the Large.

We conducted a large number of controlled continuous double auction experiments to reproduce and stress-test the phenomenon of convergence to competitive equilibrium under private information. A common finding across a total of 104 markets (involving over 1,700 subjects and over 100 markets) is convergence after a handful of trading periods. Initially, however, there is evidence for an inherent asymmetry that favors buyers, which is expressed in symmetric markets by deal prices that are significantly below equilibrium prices. Analysis of over 80,000 observations of individual bids and asks helps identify several empirical ingredients contributing to the observed phenomena including higher initial aggressiveness amongst buyers than sellers.

Not necessarily! With openly available state-of-the-art data, we uncover new and significant evidence against minimax in both professional tennis and football.

Coming soon. 😃

Let G be a finite plane multigraph and G' its dual. Each edge e of G is interpreted as a resistor of resistance Re, and the dual edge e' is assigned the dual resistance Re' :=1 / Re. Then the equivalent resistance re over e and the equivalent resistance re' over e' satisfy re / Re+re' / Re'=1. We provide a graph theoretic proof of this relation by expressing the resistances in terms of sums of weights of spanning trees in G and G' respectively. 

Yale/Virtual (1st Conference on Zero/Minimal Intelligence Agents), Zurich (Computation and Economics Research Seminar)

I also supervised the study center for undergraduates.