Marek Pycia

Stability and Preference Alignment in Matching and Coalition Formation

We study frictionless matching and coalition formation environments. Agents have preferences over coalitions, and these preferences vary with an underlying, and commonly known, state of nature. Assuming that there is substantial variability of preferences, we show that there exists a core stable coalition structure in every state of nature if, and only if, agents’ preferences are pairwise-aligned in every state of nature. In particular, we establish that there is a stable coalition structure if agents’ preferences are generated by Nash bargaining over coalitional outputs. Looking at all stability-inducing rules for sharing outputs, we show that all of them may be represented by a profile of agents’ bargaining functions, and that agents match assortatively with respect to these bargaining functions. We thus show that assortativeness is inherently related to stability, rather than being driven by particular modeling choices of agents’ sharing of output. The framework allows us to show that the presence of complementarities and peer effects – two important phenomena whose analysis was missing from prior theoretical work on matching – overturns some of the well-known comparative statics of many-to-one matching.

Dynamic inconsistency and self-control: a planner-doer interpretation

We show that Gul and Pesendorfer’s [Econometrica 69 (2001) 1403] representation result for preferences with temptation and self-control can be reexpressed in terms of a costly intrapersonal conflict between a Planner and Doer, as in Thaler and Shefrin [J. Political Econ. 89 (1981) 392] and psychologists’ standard view of self-control problems.

Incentive Compatible Allocation and Exchange of Discrete Resources

Allocation and exchange of discrete resources such as kidneys, school seats, and many other resources for which agents have single-unit demand is conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns in designing such mechanisms. We show that a mechanism is indi- vidually strategy-proof and always selects the efficient outcome with respect to some Arrovian social welfare function if and only if the mechanism is group strategy-proof and Pareto efficient. We construct the full class of these mechanisms and show that each of them can be implemented by endowing agents with control rights over resources. This new class, which we call trading cycles, contains new mechanisms as well as known mechanisms such as top trading cycles, serial dictatorships, and hierarchical exchange. We illustrate how one can use our construction to show what can and what cannot be achieved in a variety of allocation and exchange problems, and we provide an example in which the new trading-cycles mechanisms strictly Lorenz dominate all previously known mechanisms.

Ordinal Efficiency, Fairness, and Incentives in Large Markets

Efficiency and symmetric treatment of agents are the primary goals of resource allocation in environments without transfers. Focusing on ordinal mecha- nisms in which no small group of agents can substantially change the allocations of others, we show that all asymptotically efficient, symmetric, and asymptotically strategy-proof mechanisms lead to the same allocations in large markets. In particular, many mechanisms — both well-known and newly developed — are allocationally equivalent. This equivalence is consistent with prior empirical findings that different mechanisms lead to similar allocations in school choice. We also show that uniform randomizations over deterministic efficient mechanisms are asymptotically efficient.

Outside Options and the Failure of the Coase Conjecture

A buyer wishes to purchase a good from a seller who chooses a sequence of prices over time. In each period, the buyer can also exercise an outside option such as moving onto another seller. We show there is a unique equilibrium in which the seller charges a constant price in every period equal to the monopoly price against their residual demand. This result contravenes the Coase conjecture.

Matching with Externalities

We incorporate externalities into the stable matching theory of two-sided markets. Extending the classical substitutes condition to allow for externalities, we establish that stable matchings exist when agent choices satisfy substitutability. In addition, we show that the standard insights of matching theory, like the existence of side-optimal stable matchings and the deferred acceptance algorithm, remain valid despite the presence of externalities even though the standard fixed-point techniques do not apply. Furthermore, we establish novel comparative statics on externalities.

The Cost of Ordinality

School districts and other institutions allocating objects without the use of transfers tend to rely on mechanisms that only elicit agents’ ordinal preferences. The present note shows that the welfare loss imposed by only eliciting ordinal preferences can be arbitrarily large.

Efficient Bilateral Trade

We re-examine the canonical question of Myerson and Satterthwaite (1983) whether two parties can trade an indivisible good in a Pareto efficient way when they are both privately-informed about their valuations for the good. Relaxing the assumption that utilities are quasi-linear, we show that efficient trade is generically possible if agents’ utility functions are not too responsive to private information. In natural examples efficient trade is possible even when agents’ utility functions are highly responsive to their private information. The analysis relies on new methods we introduce.

Prices and Efficient Assignments Without Transfers

We study the assignment of indivisible objects in environments, such as school choice, in which transfer payments are not used. Our main result shows that every efficient assignments can be decentralized through prices. We thus establish the Second Welfare Theorem for the no-transfer environments with possibly satiated agents. The result builds on a new Separating Hyperplane Theorem, which is of independent interest.

Trading Cycles for School Choice

In this note we study the allocation and exchange of discrete resources in environments in which monetary transfers are not allowed. We allow each discrete resource to be represented by several copies, extend onto this environment the trading cycles mechanisms of Pycia and Unver [2009], and show that the extended mechanisms are Pareto efficient and strategy-proof. In particular, we construct the counterpart of Papai [2000] hiererachical exchange mechanisms for environments with copies.