
on Economic Design 
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 onetoone 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 realworld matching markets. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.06046&r=all 
By:  Herings, P. JeanJacques (RS: GSBE Theme DataDriven DecisionMaking, 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 myopicfarsighted 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 topcoalition property. For general matching problems where all women are farsighted, there is only one core element that can belong to the pairwise myopicfarsighted stable set, the womanoptimal stable matching, so all other stable outcomes are excluded for sure. If the womanoptimal 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, nonbossy, and implementable in obviously strategyproof (OSP) mechanisms. As corollaries of our result, we obtain a characterization of OSPimplementable fixed priority top trading cycles (FPTTC) rules, hierarchical exchange rules, and trading cycles rules. Troyan (2019) provides a characterization of OSPimplementable FPTTC rules when there are equal number of individuals and objects. Our result generalizes this for arbitrary values of those. 
Keywords:  Assignment problem; Obvious strategyproofness; Pareto efficiency; Nonbossiness; 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 actionformat 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 secondprice 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 secondprice 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 tradeoff between nondiscrimination 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 FrancheComté, F25000 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 wellstudied scoring voting rules in the case of small number of alternatives and large electorates under a wellknown assumption on individual preference profiles. 
JEL:  D71 D72 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:202008&r=all 