
on Economic Design 
Issue of 2022‒12‒19
six papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford 
By:  Taro Kumano (Yokohama National University, Department of Economics); Morimitsu Kurino (Keio University, Faculty of Economics) 
Abstract:  In designing prioritybased matching problems, such as school choice, the quota of each school is, to some extent, a design variable for a market designer. We define an expost studentoptimal stable matching (ESOSM) as a matching that is stable at some implementable quota distribution, and is not Pareto dominated by any stable matching among all implementable quota distributions. A simple question is whether the total resources subject to several constraints are optimally distributed in the above sense. As optimal quota distributions vary depending on students f preferences realized, no predetermined quota distribution is optimal for all of the students f preferences. This requires a new matching mechanism design for the variable quota distributions. We propose the novel mechanism called quota adjustment process (QAP), which endogenously finds an ESOSM and the corresponding optimal quota distribution for any preferences and any initial quota distribution. To put this into practice, we proposed the QAP in the process of admission reform at the University of Tsukuba in Japan. Our proposal was officially approved and implemented at the University of Tsukuba in 2021. 
Keywords:  quota adjustment process;stability;deferred acceptance mechanism;effciency;quotaadjustment stable improvement cycles 
JEL:  C78 D47 D78 I21 
Date:  2022–11–22 
URL:  http://d.repec.org/n?u=RePEc:keo:dpaper:2022016&r=des 
By:  Yu Zhou; Shigehiro Serizawa 
Abstract:  In multiobject auction models with unitary demand agents, if agents' utility functions satisfy quasilinearity, three auction formats, sealedbid auction, exact ascending auction, and approximate ascending auction, are known to identify the minimum price equilibrium (MPE), and exhibit elegant efficiency and incentivecompatibility. These auctions are conjured to preserve their properties beyond quasilinearity. Nevertheless, we exemplify that with general utility functions, these auctions fail to identify the MPEs and are substantially inefficient and manipulatable. The implications of our negative results for multiobject auction models with agents with multiunit demand, and matching with contracts models are also discussed. 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1116r&r=des 
By:  Sosung Baik; SungHa Hwang 
Abstract:  We study the revenue comparison problem of auctions when the seller has a maxmin expected utility preference. The seller holds a set of priors around some reference belief, interpreted as an approximating model of the true probability law or the focal point distribution. We develop a methodology for comparing the revenue performances of auctions: the seller prefers auction X to auction Y if their transfer functions satisfy a weak form of the singlecrossing condition. Intuitively, this condition means that a bidder's payment is more negatively associated with the competitor's type in X than in Y. Applying this methodology, we show that when the reference belief is independent and identically distributed (IID) and the bidders are ambiguity neutral, (i) the firstprice auction outperforms the secondprice and allpay auctions, and (ii) the secondprice and allpay auctions outperform the war of attrition. Our methodology yields results opposite to those of the Linkage Principle. 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2211.12669&r=des 
By:  Chao Huang 
Abstract:  A firmworker hypergraph consists of edges in which each edge joins a firm and its possible staff. We show that a stable matching exists in both discrete manytoone matching and manytoone matching with continuous transfers and quasilinear utilities when the firmworker hypergraph is balanced. Firms' preferences satisfying this condition arise in a problem of matching specialized firms with specialists. 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2211.06887&r=des 
By:  Danilov, Vladimir; Karzanov, Alexander 
Abstract:  We consider a hypergraph (I, C), with possible multiple (hyper)edges and loops, in which the vertices i ∈ I are interpreted as agents, and the edges c ∈ C as contracts that can be concluded between agents. The preferences of each agent i concerning the contracts where i takes part are given by use of a choice function fi possessing the socalled path independent property. In this general setup we introduce the notion of stable network of contracts. The paper contains two main results. The first one is that a general problem on stable systems of contracts for (I, C, f) is reduced to a set of special ones in which preferences of agents are described by use of socalled weak orders, or utility functions. However, for a special case of this sort, the stability may not exist. Trying to overcome this trouble when dealing with such special cases, we introduce a weaker notion of metastability for systems of contracts. Our second result is that a metastable system always exists. 
Keywords:  Plott choice functions, AizermanMalishevski theorem, stable marriage, roommate problem, Scarf lemma 
JEL:  C71 C78 D74 
Date:  2022–11–29 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:115482&r=des 
By:  Yingkai Li; Aleksandrs Slivkins 
Abstract:  The difficulty of recruiting patients is a wellknown issue in clinical trials which inhibits or sometimes precludes them in practice. We incentivize participation in clinical trials by leveraging information asymmetry between the trial and the patients. We obtain an optimal solution in terms of the statistical performance of the trial, as expressed by an estimation error. Namely, we provide an incentivecompatible mechanism with a particular guarantee, and a nearly matching impossibility result for any incentivecompatible mechanism. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.06191&r=des 