
on Economic Design 
By:  William PHAN; Ryan TIERNEY; Yu ZHOU 
Abstract:  We consider the problem of matching students to schools when students are able to express preferences over crowding. For example, schools have varying per capita expenditures, average teacherstudent ratios, etc. These characteristics of a school are now endogenously determined—matchings with more students to a particular school decrease each of the variables above. We propose a new equilibrium notion, the Rationing Crowding Equilibrium (RCE), that accommodates crowding, noenvy, and respect for priorities. We prove the existence of RCE under mild domain conditions, and establish a Rural Hospitals Theorem and welfare lattice result on the set of RCE. The latter implies the existence of a maximal RCE, and that such RCE are studentoptimal. Moreover, the mechanism defined by selection from the maximal RCE correspondence is strategyproof. We also identify an algorithm to find a maximal RCE for a natural subdomain. 
Keywords:  School choice with crowding; Rationing crowding equilibrium; Student optimality;Strategyproofness 
JEL:  C78 D47 D62 I20 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:kue:epaper:e21006&r= 
By:  Martin F. Hellwig (Max Planck Institute for Research on Collective Goods) 
Abstract:  Anonymous social choice function for a large atomless population maps crosssection distributions of preferences into outcomes. Because any one individual is too insignificant to a¤ect these distributions, every anonymous social choice function is individually strategyproof. However, not every anonymous social choice function is group strategyproof. If the set of outcomes is linearly ordered and participants have singlepeaked preferences, an anonymous social choice function is group strategyproof if and only if it can be implemented by a mechanism involving binary votes between neighbouring outcomes with nondecreasing thresholds for "moving higher up". Such a mechanism can be interpreted as a version of Moulin's (1980) generalized medianvoter mechanism for a large population. 
Keywords:  Social choice, large populations, strategy proofness, group strategy proofness, singlepeaked preferences 
Date:  2021–10–13 
URL:  http://d.repec.org/n?u=RePEc:mpg:wpaper:2021_18&r= 
By:  Chiara Donnini (Università di Napoli Parthenope); Maria Laura Pesce (Università di Napoli Federico II and CSEF) 
Abstract:  We consider the notion of strict fairness, introduced by Zhou (1992), which requires, besides efficiency, that no agent prefers (or envies) the average bundle of any coalition to her bundle. We investigate the size of envied coalitions and if the set of strictly fair allocations changes because a limitation on the coalition formation is imposed. The study is conducted in atomless economies as well as in the socalled mixed markets. 
Keywords:  Fairness, Envyfreeness, Equalincome Walrasian allocations, Coalitions. 
JEL:  D51 D63 D71 C02 
Date:  2021–09–29 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:624&r= 
By:  Marleen Marra (ECON  Département d'économie (Sciences Po)  Sciences Po  Sciences Po  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  This paper presents, solves, and estimates the first structural auction model with seller selection. This allows me to quantify network effects arising from endogenous bidder and seller entry into auction platforms, facilitating the estimation of theoretically ambiguous fee impacts by tracing them through the game. Relevant model primitives are identified from variation in secondhighest bids and reserve prices. My estimator builds off the discrete choice literature to address the double nested fixed point characterization of the entry equilibrium. Using new wine auction data, I estimate that this platform's revenues increase up to 60% when introducing a bidder discount and simultaneously increasing seller fees. More bidders enter when the platform is populated with lowerreserve setting sellers, driving up prices. Moreover, I show that meaningful antitrust damages can be estimated in a platform setting despite this twosidedness. 
Keywords:  Auctions with entry,Twosided markets,Nonparametric identification,Estimation,Nested fixed point 
Date:  2019–12–01 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03393068&r= 
By:  Andrea Attar (CEIS & DEF University of Rome "Tor Vergata" and Toulouse School of Economics); Eloisa Campioni (CEIS & DEF University of Rome "Tor Vergata" and Toulouse School of Economics); Thomas Mariotti (Toulouse School of Economics, CNRS); Alessandro Pavan (Northwestern University, Evanston) 
Abstract:  We study games in which several principals contract with several privatelyinformed agents. We show that enabling the principals to engage in contractible private disclosures {by sending private signals to the agents about how the mechanisms will respond to the agents' messages { can significantly affect the predictions of such games. Our first result shows that private disclosures may generate equilibrium outcomes that cannot be supported in any game without private disclosures, no matter the richness of the message spaces and the availability of public randomizing devices. The result thus challenges the canonicity of the universal mechanisms of Epstein and Peters (1999). Our second result shows that equilibrium outcomes of games without private disclosures need not be sustainable when private disclosures are allowed. The result thus challenges the robustness of the \folk theorems" of Yamashita (2010) and Peters and TroncosoValverde (2013). These findings call for a novel approach to the analysis of competingmechanism games. 
Keywords:  Incomplete Information, Competing Mechanisms, Private Disclosures, Signals, Universal Mechanisms, Folk Theorems. 
JEL:  D82 
Date:  2021–10–21 
URL:  http://d.repec.org/n?u=RePEc:rtv:ceisrp:519&r= 
By:  Martin F. Hellwig (Max Planck Institute for Research on Collective Goods) 
Abstract:  The paper studies efficient publicgood provision in a model with private values whose distribution depends on a macro shock; conditionally on this shock, values are independent and identically distributed. A generalization of the Bayesian mechanism of d'Aspremont and GérardVaret is shown to implement an efficient provision rule with budget balance. However, firstbest implementation and budget balance are incompatible with a reqruirement of weak robustness whereby incentive compatibility of the mechanism is independent of the stochastic specification within the class of specifications defined by the structure of the model. Budget imbalances with robust implementation are small if there are many participants, as surplus from the ClarkeGroves mechanism converges to zero in probability when the number of participants becomes large. In the limit, with a continuum of agents, a firstbest provision rule with equal cost sharing is robustly incentivecompatible. In this limit, information about the macro shock, which is the only thing that matters for publicgood provision, can be elicited without any efficiency loss. 
Keywords:  Efficient publicgood provision, incomplete information, conditionally independent private values, macro uncertainty, budget balance, weakly robust incentive compatibility 
Date:  2021–10–13 
URL:  http://d.repec.org/n?u=RePEc:mpg:wpaper:2021_19&r= 