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on Economic Design |
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Issue of 2022‒02‒28
seven papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Julien Combe (École Polytechnique); Umut Mert Dur (North Carolina State University); Olivier Tercieux (Paris School of Economics); Camille Terrier (University of Lausanne); M. Utku Ünver (Boston College) |
| Abstract: | Centralized (re)assignment of workers to jobs is increasingly common in public and private sectors. These markets often suffer from distributional problems. To alleviate these, we propose two new strategy-proof (re)assignment mechanisms. While they both improve individual and distributional welfare over the status quo, one achieves two-sided efficiency and the other achieves a novel fairness property. We quantify the performance of these mechanisms in teacher (re)assignment where unequal distribution of experienced teachers in schools is a widespread concern. Using French data, we show that our efficient mechanism reduces the teacher experience gap across regions more effectively than benchmarks, including the current mechanism, while also effectively increasing teacher welfare. As an interesting finding, while our fairness-based mechanism is very effective in reducing teacher experience gap, it prevents the mobility of tenured teachers, which is a detrimental teacher welfare indicator. |
| Keywords: | Matching Theory, Market Design, Priority Design, Teacher Reassignment, Status- quo Improvement, Fairness, Efficiency, Distributional Welfare Measures |
| JEL: | C78 D50 D61 I21 |
| Date: | 2022–02–15 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:1050&r= |
| By: | Federico Echenique; Sumit Goel; SangMok Lee |
| Abstract: | We study discrete allocation problems, as in the textbook notion of an exchange economy, but with indivisible goods. The problem is well-known to be difficult. The model is rich enough to encode some of the most pathological bargaining configurations in game theory, like the roommate problem. Our contribution is to show the existence of stable allocations (outcomes in the weak core, or in the bargaining set) under different sets of assumptions. Specifically, we consider dichotomous preferences, categorical economies, and discrete TU markets. The paper uses varied techniques, from Scarf's balanced games to a generalization of the TTC algorithm by means of Tarski fixed points. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.04706&r= |
| By: | Devansh Jalota |
| Abstract: | We study two-sided many-to-one matching markets with transferable utilities, e.g., labor and rental housing markets, in which money can exchange hands between agents, subject to distributional constraints on the set of feasible allocations. In such markets, we establish the efficiency of equilibrium arrangements, specified by an assignment and transfers between agents on the two sides of the market, and study the conditions on the distributional constraints and agent preferences under which equilibria exist. To this end, we first consider the setting when the number of institutions (e.g., firms in a labor market) is one and show that equilibrium arrangements exist irrespective of the nature of the constraint structure or the agents' preferences. However, equilibrium arrangements may not exist in markets with multiple institutions even when agents on each side have linear (or additively separable) preferences over agents on the other side. Thus, for markets with linear preferences, we study sufficient conditions on the constraint structure that guarantee the existence of equilibria using linear programming duality. Our linear programming approach not only generalizes that of Shapley and Shubik (1971) in the one-to-one matching setting to the many-to-one matching setting under distributional constraints but also provides a method to compute market equilibria efficiently. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.05232&r= |
| By: | Pranay Gorantla; Kunal Marwaha; Santhoshini Velusamy |
| Abstract: | We study the problem of allocating a set $M$ of $m$ ${indivisible}$ items among $n$ agents in a fair manner. We consider two well-studied notions of fairness: envy-freeness (EF), and envy-freeness up to any good (EFX). While it is known that complete EF allocations do not always exist, it is not known if complete EFX allocations exist besides a few cases. In this work, we reformulate the problem to allow $M$ to be a multiset. Specifically, we introduce a parameter $t$ for the number of distinct ${types}$ of items, and study allocations of multisets that contain items of these $t$ types. We show the following: 1. For arbitrary $n$, $t$, a complete EF allocation exists when agents have distinct additive valuations, and there are ${enough}$ items of each type. 2. For arbitrary $n$, $m$, $t$, a complete EFX allocation exists when agents have additive valuations with identical ${preferences}$. 3. For arbitrary $n$, $m$, and $t\le2$, a complete EFX allocation exists when agents have additive valuations. For 2 and 3, our approach is constructive; we give a polynomial-time algorithm to find a complete EFX allocation. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.05186&r= |
| By: | Pablo Amorós (Departamento de Teoría e Historia Económica, Universidad de Málaga.) |
| Abstract: | We consider the problem of a group of experts who have to rank a set of candidates. Society's optimal choice relies on experts?honest judgments about the deserving ranking. However, experts' judgments are impossible to verify. Moreover, experts' judgments do not entirely determine their preferences. Then, experts might want to misreport their judgments if, by doing so, some ranking that they like best is selected. To solve this problem, we have to design a mechanism where the experts interact so that the socially optimal ranking is implemented. Whether this is possible depends on (1) how experts' judgments are aggregated to determine the socially optimal ranking and (2) how experts' preferences relate to their judgments. We state necessary and su¢ cient conditions on these two elements for the socially optimal ranking to be implementable in dominant strategies and Nash equilibrium. Then, we study the implementability of some widely used judgment aggregation rules, including extensions of scoring and Condorcet consistent voting rules. Finally, we propose a non-trivial judgment aggregation rule that is Nash implementable. |
| Keywords: | Evaluation; impartiality; manipulability; ranking of candidates; mechanism design; voting rules. |
| JEL: | C72 D71 D78 |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2022-1&r= |
| By: | Finn Schmieter |
| Abstract: | This paper analyses the role of timing in common-value elections. There are two voting periods where voters can decide for themselves when to publicly cast their votes after receiving private signals. In welfare-optimal equilibria, agents use their timing to communicate the strength of their private information to the other voters. This communication allows for better information aggregation than simultaneous voting or voting with exogenously fixed timing. In the case of a simple majority voting rule, a second voting period mitigates the Swing Voter’s Curse more effectively than abstention. |
| Keywords: | Elections, Pivotal Voting, Communication, Information |
| JEL: | D72 D82 D83 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_328&r= |
| By: | Siyang Xiong |
| Abstract: | We provide a necessary and sufficient condition for rationalizable implementation of social choice functions, i.e., we offer a complete answer regarding what social choice functions can be rationalizably implemented. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.04885&r= |