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 (revision requested by the American Economic Review)

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.

Demand Reduction, Inefficiency and Revenues 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 primary goals of allocation of resources such as school seats. We show that in large markets without transfers all symmetric, efficient, and asymptotically strategy-proof ordinal allocation mechanisms coincide asymptotically. In particular, this implies that in large markets symmetric ordinal mechanisms we do not yet know cannot improve upon the mechanisms we already know and use. We also provide the first general criterion for asymptotic ordinal efficiency: uniform randomizations over deterministic efficient mechanisms are asymptotically ordinally efficient. This resolves in positive the long-standing question whether standard ordinal mechanisms are asymptotically ordinally efficient.

Related note: Ordinal Efficiency, Fairness, and Incentives in Large Multi-Unit-Demand Assignments, with Qingmin Liu (extends results of the main paper to multiple-unit demands)

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.

Optimal Bundling (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.