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on Economic Design |
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Issue of 2020‒11‒30
seven papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Muhammad Maaz |
| Abstract: | A bipartite graph consists of two disjoint vertex sets, where vertices of one set can only be joined with an edge to vertices in the opposite set. Hall's theorem gives a necessary and sufficient condition for a bipartite graph to have a saturating matching, meaning every vertex in one set is matched to some vertex in the other in a one-to-one correspondence. When we imagine vertices as agents and let them have preferences over other vertices, we have the classic stable marriage problem introduced by Gale and Shapley, who showed that one can always find a matching that is stable with respect to agent's preferences. These two results often clash: saturating matchings are not always stable, and stable matchings are not always saturating. I prove a simple necessary and sufficient condition for every stable matching being saturating for one side. I show that this result subsumes and generalizes some previous theorems in the matching literature. I find a necessary and sufficient condition for stable matchings being saturating on both sides, also known as perfect matchings. These results could have important implications for the analysis of numerous real-world matching markets. |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2011.06046&r=all |
| By: | Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics); Mauleon, Ana; Vannetelbosch, V. |
| Abstract: | We consider marriage problems where myopic and farsighted players interact. To study such problems, we use the pairwise myopic-farsighted stable set. Blocking occurs by coalitions of size one or two. We require that all blocking players should strictly improve. We pay particular attention to the question whether core elements survive in this environment. This is the case when all players are myopic as well as when all players are farsighted. It also holds for matching problems satisfying the top-coalition property. For general matching problems where all women are farsighted, there is only one core element that can belong to the pairwise myopic-farsighted stable set, the woman-optimal stable matching, so all other stable outcomes are excluded for sure. If the woman-optimal stable matching is dominated from the woman point of view by an individually rational matching, then the pairwise myopic farsighted stable set cannot contain a core element. We show that blocking by coalitions of arbitrary size leads to identical results. |
| JEL: | C70 C78 |
| Date: | 2020–11–16 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2020031&r=all |
| By: | Mandal, Pinaki; Roy, Souvik |
| Abstract: | We consider assignment problems where individuals are to be assigned at most one indivisible object and monetary transfers are not allowed. We provide a characterization of assignment rules that are Pareto efficient, non-bossy, and implementable in obviously strategy-proof (OSP) mechanisms. As corollaries of our result, we obtain a characterization of OSP-implementable fixed priority top trading cycles (FPTTC) rules, hierarchical exchange rules, and trading cycles rules. Troyan (2019) provides a characterization of OSP-implementable FPTTC rules when there are equal number of individuals and objects. Our result generalizes this for arbitrary values of those. |
| Keywords: | Assignment problem; Obvious strategy-proofness; Pareto efficiency; Non-bossiness; Indivisible goods |
| JEL: | C78 D82 |
| Date: | 2020–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:104044&r=all |
| By: | Wu, Haoyang |
| Abstract: | In mechanism design theory, a designer would like to implement a social choice function which specifies her favorite outcome for each possible profile of agents' private types. The revelation principle asserts that if a social choice function can be implemented by a mechanism in equilibrium, then there exists a direct mechanism that can truthfully implement it. This paper aims to propose a failure of the revelation principle. At first we point out that in any game the format of each agent's strategy is either an abstract message or a real action. For any given social choice function, if the mechanism which implements it in Bayesian Nash equilibrium has action-format strategies, then ``honest and obedient'' will not be an equilibrium strategy in the corresponding direct mechanism. Consequently, the revelation principle fails. |
| Keywords: | Mechanism design; Revelation principle. |
| JEL: | D71 |
| Date: | 2020–11–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:104171&r=all |
| By: | Olivier Bos; Tom Truyts |
| Abstract: | We study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders’ types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in the second-price auction and the English auction. We establish there is no equivalence between these two auction designs, neither in bidding strategies nor in expected revenue. This is because the presence or absence of an increasing price clock, affects signaling incentives differently in both auction formats, and thereby also the bidders’ incentives to overbid their types. This leads to a strictly higher expected revenue in the second-price auction than in the English auction. Our analysis is completed by a comparison with other disclosure policies. Applications include art auctions and charity auctions. |
| Keywords: | costly signalling, D1 criterion, social status, art auctions, charity auctions |
| JEL: | D44 D82 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8650&r=all |
| By: | Nicolas Fugger; Vitali Gretschko; Helene Mass; Achim Wambach |
| Abstract: | Procurement regulation aimed at curbing discrimination requires equal treatment of sellers. However, Deb and Pai show that such regulation imposes virtually no restrictions on the ability to discriminate. We propose a simple rule - imitation perfection - that restricts discrimination significantly. It ensures that in every equilibrium bidders with the same valuation distribution and the same valuation earn the same expected utility. If all bidders are homogeneous, revenue and social surplus optimal auctions consistent with imitation perfection exist. For heterogeneous bidders, however, it is incompatible with revenue and social surplus optimization. Thus, a trade-off between non-discrimination and optimality exists. |
| Keywords: | Discrimination, symmetric auctions, procurement regulation |
| JEL: | D44 D73 D82 L13 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_225v1&r=all |
| By: | Mostapha Diss (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France); Boris Tsvelikhovskiy (Department of Mathematics, Northeastern University, Boston, MA, 02115, USA) |
| Abstract: | Coalitional manipulation in voting is considered to be any scenario in which a group of voters decide to misrepresent their vote in order to secure an outcome they all prefer to the first outcome of the election when they vote honestly. The present paper is devoted to study coalitional manipulability within the class of scoring voting rules. For any such rule and any number of alternatives, we introduce a new approach allowing to characterize all the outcomes that can be manipulable by a coalition of voters. This gives us the possibility to find the probability of manipulable outcomes for some well-studied scoring voting rules in the case of small number of alternatives and large electorates under a well-known assumption on individual preference profiles. |
| JEL: | D71 D72 |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2020-08&r=all |