Marek Pycia's Website

Marek Pycia

Assistant Professor of Economics

UCLA

9371 Bunche Hall

Los Angeles, CA 90095

pycia-at-ucla-dot-edu

Research

Stability and Preference Alignment in Matching and Coalition Formation, Econometrica 80(1) (2012), 323-362.

In a broad class of matching and coalition formation environments agents' preferences over coalitions depend on an underlying, and commonly known, state of nature. Allowing for complementarities and peer effects, and assuming that there is substantial variability of preferences across states of nature, we show that there exists a core stable coalition structure in every state if and only if agents’ preferences are pairwise-aligned in every state. This implies that there is a stable coalition structure if agents’ preferences are generated by Nash bargaining over coalitional outputs. We further show that all stability-inducing rules for sharing outputs can be represented by a profile of agents’ bargaining functions, and that agents match assortatively with respect to these bargaining functions. This framework allows us to show how complementarities and peer effects overturn well-known comparative statics of many-to-one matching.

Earlier versions – Many-to-One Matching with Complementarities and Peer Effects, Many-to-One Matching without Substitutability (MIT IPC Working Paper 2005/08), Bargaining and Coalition Formation – available upon request

Outside Options and the Failure of the Coase Conjecture, with Simon Board, American Economic Review, accepted

A buyer wishes to purchase a good from a seller who chooses a sequence of prices over time. Each period the buyer can also exercise an outside option, abandoning their search or moving on to 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, contravening the Coase conjecture. We then embed the single-firm model into a search framework and show the result provides a foundation for the usual “no haggling” assumption.

Older draft (provides details on search with correlated types)

Demand Reduction and Inefficiency in Multi-Unit Auctions, with Larry Ausubel, Peter Cramton, Marzena Rostek, and Marek Weretka (resubmission requested by the Review of Economic Studies)

Uniform-price and pay-as-bid auctions are the most common formats for selling divisible goods. Most Treasury departments use one of the two designs to auction securities on a weekly basis. This paper establishes inefficiency of the uniform-price auction, ambiguity of revenue rankings in general environments, and for the linear Bayesian Nash Equilibrium, revenue rankings for the uniform-price, the pay-as-bid and Vickrey auctions.

Incentive Compatible Allocation and Exchange of Discrete Resources, with Utku Unver

Allocation and exchange of many discrete resources – such as kidneys or school seats – is conducted via direct mechanisms without monetary transfers. A primary concern in designing such mechanisms is the coordinated strategic behavior of market participants and its impact on resulting allocations. To assess the impact of this implementation constraint, we construct the full class of group dominant-strategy incentive compatible and Pareto efficient mechanisms. We call the mechanisms “Trading Cycles.” This class contains new mechanisms as well as such previously studied mechanisms as top trading cycles, serial dictatorships, and hierarchical exchange. In some problems, the new trading-cycles mechanisms perform better than all previously known mechanisms. Just as importantly, knowing that all group incentive-compatible and efficient mechanisms can be implemented as trading cycles allows us to easily determine which efficient outcomes can and cannot be achieved in a group incentive-compatible way.

Related note: Trading Cycles for School Choice, with Utku Unver (extends Trading Cycles to environments with object copies)

Ordinal Efficiency, Fairness, and Incentives in Large Markets, with Qingmin Liu

Efficiency and symmetric treatment of agents are the primary goals of allocation of resources in environments without transfers. Focusing on ordinal mechanisms in which no small group of agents can substantially change the allocation of others, we first show that uniform randomizations over deterministic efficient mechanisms are asymptotically ordinally efficient, that is, efficient ex ante. This implies that ordinal efficiency and ex-post Pareto efficiency become equivalent in large markets, and that many standard mechanisms are asymptotically ordinally efficient. Second, we show that all asymptotically ordinally efficient, symmetric, and asymptotically strategy-proof mechanisms lead to the same allocations in large markets.

Related notes: Assignment with Multiple-Unit Demands and Responsive Preferences (introduces the framework of multiple-unit allocation with responsive preferences), Ordinal Efficiency, Fairness, and Incentives in Large Multi-Unit-Demand Assignments, with Qingmin Liu, (extends the results of the main paper to multiple-unit demands). See the older draft for a small-market characterization of Probabilistic Serial

Dynamic Inconsistency and Self-Control: A Planner-Doer Interpretation, with Roland Bénabou, Economic Letters 77(3) (2002), 419-424.

We show that Gul and Pesendorfer’s [Econometrica 69 (2001)] 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)] and psychologists’ standard view of self-control problems.

Stochastic vs Deterministic Mechanisms in Multidimensional Screening, my Toulouse DEEQA (M.Phil.) thesis Generic Optimality of Stochastic Mechanisms in Multidimensional Screening, with some later additions and edits

Refereed Publications in Mathematics (from my college and high-school days)

‘‘Linear Functional Inequalities,’’ Dissertationes Mathematicae 438 (2006), 1-62.

‘‘A Short Proof of the Regularity of s-Convex Functions,’’ Aeaquationes Mathematicae 61 (2001), No. 1-2, 128-130.

‘‘A Convolution Inequality,’’ Aeaquationes Mathematicae 57 (1999), No. 2-3, 185-200.

‘‘Positive Homogeneous Functionals Related to Lp-Norms,’’ with J. Matkowski, Journal of Mathematical Analysis and Applications 200 (1996), 245-253.

‘‘On the Volume of Convex Hulls of Sets on Spheres,’’ with R. Latała, Geometriae Dedicata 63 (1996), 153-157.

‘‘A Proof of a Conjecture of Bobkov and Houdré,’’ with S. Kwapień i W. Schachermayer, Electronic Communications in Probability 1 (1996), paper 2.

‘‘On (α,a)-Convex Functions,’’ with J. Matkowski, Archiv der Mathematik 64 (1995), 132-138.

‘‘Convex-like Inequality, Homogeneity and a Characterization of Lp-Norm,’’ with J. Matkowski, Annales Polonici Mathematici 60 (1995), 221-230.

‘‘On a General Solution of Finite Order Difference Equations with Constant Coefficients,’’ Archivum Mathematicum 28 (1992), 237-240.