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on Economic Design |
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Issue of 2021‒08‒23
six papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Marcelo A. Fernandez; Kirill Rudov; Leeat Yariv |
| Abstract: | We study the impacts of incomplete information on centralized one-to-one matching markets. We focus on the commonly used Deferred Acceptance mechanism (Gale and Shapley, 1962). We show that many complete-information results are fragile to a small infusion of uncertainty about others' preferences. |
| JEL: | C78 D47 D82 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29043&r= |
| By: | Felix Brandt; Patrick Lederer |
| Abstract: | Gibbard and Satterthwaite have shown that the only single-valued social choice functions (SCFs) that satisfy non-imposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by misrepresenting their preferences) are dictatorships. In this paper, we consider set-valued social choice correspondences (SCCs) that are strategyproof according to Fishburn's preference extension and, in particular, the top cycle, an attractive SCC that returns the maximal elements of the transitive closure of the weak majority relation. Our main theorem implies that, under mild conditions, the top cycle is the only non-imposing strategyproof SCC whose outcome only depends on the quantified pairwise comparisons between alternatives. This result effectively turns the Gibbard-Satterthwaite impossibility into a complete characterization of the top cycle by moving from SCFs to SCCs. It is obtained as a corollary of a more general characterization of strategyproof SCCs. |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2108.04622&r= |
| By: | Ryosuke Sakai; Shigehiro Serizawa |
| Abstract: | We consider the multi-object allocation problem with monetary transfers where each agent obtains at most one object (unit-demand). We focus on allocation rules satisfying individual rationality, no subsidy, efficiency, and strategy-proofness. Extending the result of Morimoto and Serizawa (2015), we show that for an arbitrary number of agents and objects, the minimum price Walrasian is characterized by the four properties on the classical domain. |
| Date: | 2021–06 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1134&r= |
| By: | Xu Lang; Zaifu Yang |
| Abstract: | We examine the implementation of reduced-form allocation rules that assign multiple indivisible objects to many agents, with incomplete information and distributional constraints across objects and agents. To obtain implementability results, we adopt a lift-and-project approach, which enables us to and a general condition called total unimodularity, a well-recognized class of matrices with simple entries of -1, 0, or 1. This condition yields several new and general characterization results including those on hierarchies, bihierarchies, and consecutiveness. Our model and results extend and unify many well-known ones considerably, find new applications, and also apply to both ordinal and cardinal preferences. |
| Keywords: | Implementation, Reduced-form rules, Indivisible goods, Distributional constraints, Total unimodularity, Incomplete information. |
| JEL: | D44 C65 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:21/05&r= |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Edmund Yeh (Department of Electrical and Computer Engineering, Northeastern University); Jinkun Zhang (Department of Electrical and Computer Engineering, Northeastern University) |
| Abstract: | We analyze nonlinear pricing with finite information. We consider a multi-product environment where each buyer has preferences over a d-dimensional variety of goods. The seller is limited to offering a finite number n of d-dimensional choices. The limited menu reflects a finite communication capacity between the buyer and seller. We identify necessary conditions that the optimal finite menu must satisfy, for either the socially efficient or the revenue-maximizing mechanism. These conditions require that information be bundled, or "quantized," optimally. We introduce vector quantization and establish that the losses due to finite menus converge to zero at a rate of 1/n^2/^d. In the canonical model with one-dimensional products and preferences, this establishes that the loss resulting from using the n-item menu converges to zero at a rate proportional to 1/n^2. |
| Keywords: | Mechanism Design, Nonlinear Pricing, Multi-Dimension, Multi-Product, Private Information, Limited Information, Quantization, Information Theory |
| JEL: | D82 D83 D86 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2297&r= |
| By: | Rida Laraki; Estelle Varloot |
| Abstract: | In the problem of aggregating experts' probabilistic predictions over an ordered set of outcomes, we introduce the axiom of level-strategy\-proofness (level-SP) and prove that it is a natural notion with several applications. Moreover, it is a robust concept as it implies incentive compatibility in a rich domain of single-peakedness over the space of cumulative distribution functions (CDFs). This contrasts with the literature which assumes single-peaked preferences over the space of probability distributions. Our main results are: (1) a reduction of our problem to the aggregation of CDFs; (2) the axiomatic characterization of level-SP probability aggregation functions with and without the addition of other axioms; (3) impossibility results which provide bounds for our characterization; (4) the axiomatic characterization of two new and practical level-SP methods: the proportional-cumulative method and the middlemost-cumulative method; and (5) the application of proportional-cumulative to extend approval voting, majority rule, and majority judgment methods to situations where voters/experts are uncertain about how to grade the candidates/alternatives to be ranked.\footnote{We are grateful to Thomas Boyer-Kassem, Roger Cooke, Aris Filos-Ratsikas, Herv\'e Moulin, Clemens Puppe and some anonymous EC2021 referees for their helpful comments and suggestions.} \keywords{Probability Aggregation Functions \and ordered Set of Alternatives \and Level Strategy-Proofness \and Proportional-Cumulative \and Middlemost-Cumulative} |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2108.04705&r= |