
on Economic Design 
By:  Marcelo Ariel Fernandez; Kirill Rudov; Leeat Yariv 
Abstract:  We study the impacts of incomplete information on centralized onetoone matching markets. We focus on the commonly used Deferred Acceptance mechanism (Gale and Shapley, 1962). We show that many completeinformation results are fragile to a small infusion of uncertainty about others' preferences. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.04098&r= 
By:  Julien Grenet; YingHua He; Dorothea K\"ubler 
Abstract:  The matching literature often recommends market centralization under the assumption that agents know their own preferences and that their preferences are fixed. We find counterevidence to this assumption in a quasiexperiment. In Germany's university admissions, a clearinghouse implements the early stages of the GaleShapley algorithm in real time. We show that early offers made in this decentralized phase, although not more desirable, are accepted more often than later ones. These results, together with survey evidence and a theoretical model, are consistent with students' costly learning about universities. We propose a hybrid mechanism to combine the advantages of decentralization and centralization. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01532&r= 
By:  Freeman, Rupert; Pritchard, Geoffrey; Wilson, Mark 
Abstract:  We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallowsdistributed preferences for four common assignment mechanisms. 
Date:  2021–07–22 
URL:  http://d.repec.org/n?u=RePEc:osf:socarx:xt37c&r= 
By:  Jorge AlcaldeUnzu; Flip Klijn; Marc Vorsatz 
Abstract:  The theoretical literature on public school choice proposes centralized mechanisms that assign children to schools on the basis of parents' preferences and the priorities children have for different schools. The related experimental literature analyzes in detail how various mechanisms fare in terms of welfare and stability of the resulting matchings, yet often provides only aggregate statistics of the individual behavior that leads to these outcomes (i.e., the degree to which subjects tell the truth in the induced simultaneous move game). In this paper, we show that the quantal response equilibrium adequately describes individual behavior and the resulting matching in a laboratory experiment on the (constrained) immediate acceptance mechanism. Specifically, the comparative statics of the quantal response equilibrium capture the directional changes of subject behavior and the prevalence of the different stable matchings when cardinal payoffs (i.e., relative preference intensities) are modified in the experiment. 
Keywords:  laboratory experiment, school choice, immediate acceptance mechanism, Boston mechanism, quantal response equilibrium 
JEL:  C78 C91 C92 D78 I20 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:1270&r= 
By:  Max Kapur 
Abstract:  This article proposes a characterization of admissions markets that can predict the distribution of students at each school or college under both centralized and decentralized admissions paradigms. The characterization builds on recent research in stable assignment, which models students as a probability distribution over the set of ordinal preferences and scores. Although stable assignment mechanisms presuppose a centralized admissions process, I show that stable assignments coincide with equilibria of a decentralized, iterative market in which schools adjust their admissions standards in pursuit of a target class size. Moreover, deferred acceptance algorithms for stable assignment are a special case of a wellunderstood price dynamic called t\^{a}tonnement. The second half of the article turns to a parametric distribution of student types that enables explicit computation of the equilibrium and is invertible in the schools' preferability parameters. Applying this model to a public dataset produces an intuitive ranking of the popularity of American universities and a realistic estimate of each school's demand curve, and does so without imposing an equilibrium assumption or requiring the granular student information used in conventional logistic regressions. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01340&r= 
By:  Philippe Jehiel; Konrad Mierendorff 
Abstract:  We consider auction environments in which at the time of the auction bidders observe signals about their expost value. We introduce a model of novice bidders who do not know know the joint distribution of signals and instead build a statistical model relating others' bids to their own ex post value from the data sets accessible from past similar auctions. Crucially, we assume that only ex post values and bids are accessible while signals observed by bidders in past auctions remain private. We consider steadystates in such environments, and importantly we allow for correlation in the signal distribution. We first observe that datadriven bidders may behave suboptimally in classical auctions such as the secondprice or firstprice auctions whenever there are correlations. Allowing for a mix of rational (or experienced) and datadriven (novice) bidders results in inefficiencies in such auctions, and we show the inefficiency extends to all auctionlike mechanisms in which bidders are restricted to submit onedimensional (realvalued) bids. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.00640&r= 
By:  Dirk Bergemann; Alessandro Bonatti; Andreas Haupt; Alex Smolin 
Abstract:  We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing  a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a) each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested. We exhibit two distinct sets of sufficient conditions. The first set of conditions is given by a weak version of monotonicity of types and virtual values, while maintaining a regularity assumption, i.e., that the productbyproduct revenue curves are singlepeaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS)  the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption. Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer's types are monotone, the seller can equivalently post a vector of singleitem prices: upgrade pricing and separate pricing are equivalent. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.10323&r= 
By:  Lirong Xia 
Abstract:  In 1988, Moulin proved an insightful and surprising impossibility theorem that reveals a fundamental incompatibility between two commonlystudied axioms of voting: no resolute voting rule (which outputs a single winner) satisfies Condorcet Criterion and Participation simultaneously when the number of alternatives m is at least four. In this paper, we prove an extension of this impossibility theorem using smoothed analysis: for any fixed $m\ge 4$ and any voting rule r, under mild conditions, the smoothed likelihood for both Condorcet Criterion and Participation to be satisfied is at most $1\Omega(n^{3})$, where n is the number of voters that is sufficiently large. Our theorem immediately implies a quantitative version of the theorem for i.i.d. uniform distributions, known as the Impartial Culture in social choice theory. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.06435&r= 
By:  Laurent Bouton; Aniol LlorenteSaguer; Antonin Macé; Dimitrios Xefteris 
Abstract:  This paper studies voting in shareholders meetings. We focus on the informational efficiency of different voting mechanisms, taking into account that they affect both management's incentives before the meeting and shareholders' decisions at the meeting. We first focus on the case in which the management does not affect the proposal being voted on. We prove that, for any distribution of shareholdings, the oneshareonevote mechanism (1S1V) dominates the onepersononevote mechanism (1P1V), independently of whether or how shareholdings correlate with information accuracy. We also show that 1S1V becomes efficient only if votes are fully divisible. Second, we consider the case in which the management decides whether to put the proposal to a vote. The properties of a voting mechanism then depend both on its voting efficiency and on how it affects managers' incentives to select good proposals. We uncover a tradeoff between selection and voting efficiency underlying the comparison of 1S1V and 1P1V: the higher voting efficiency of 1S1V implies worse selection incentives. In some cases, the negative effect of worse selection incentives on shareholders' welfare can be large enough to wash out the higher voting efficiency of 1S1V. 
JEL:  D72 G3 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29005&r= 
By:  Yajing Chen; Zhenhua Jiao; Chenfeng Zhang 
Abstract:  This paper considers truncation strategies in housing markets. First, we characterize the top trading cycles rule in housing markets by the following two groups of axioms: individual rationality, Pareto efficiency, truncationinvariance; individual rationality, endowmentsswappingproofness, truncationinvariance. The new characterizations refine Ma (1994), Fujinaka and Wakayama (2018), and Chen and Zhao (2021) simultaneously, because truncationinvariance is weaker than both strategyproofness and rank monotonicity. Second, we show that the characterization result of the current paper can no longer be obtained by further weakening truncationinvariance to truncationproofness. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.14456&r= 
By:  Dmitry Levando 
Abstract:  We study coalition structure formation with intra and intercoalition externalities in the introduced family of nested noncooperative simultaneous finite games. A noncooperative game embeds a coalition structure formation mechanism, and has two outcomes: an allocation of players over coalitions and a payoff for every player. Coalition structures of a game are described by Young diagrams. They serve to enumerate coalition structures and allocations of players over them. For every coalition structure a player has a set of finite strategies. A player chooses a coalition structure and a strategy. A (social) mechanism eliminates conflicts in individual choices and produces final coalition structures. Every final coalition structure is a noncooperative game. Mixed equilibrium always exists and consists of a mixed strategy profile, payoffs and equilibrium coalition structures. We use a maximum coalition size to parametrize the family of the games. The noncooperative game of Nash is a partial case of the model. The result is different from the Shapley value, a strong Nash, coalitionproof equilibria, core solutions, and other equilibrium concepts. We supply few noncooperative coalition structure stability criteria. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.00711&r= 
By:  Han Xiao; Tianhang Lu; Qizhi Fang 
Abstract:  The multiple partners matching game is a cooperative profitsharing game, which generalizes the classic matching game by allowing each player to have more than one partner. The core is one of the most important concepts in cooperative game theory, which consists all possible ways of allocating the total profit of the game among individual players such that the grand coalition remains intact. For the multiple partners matching game, the core may be empty in general [Deng et al., Algorithmic aspects of the core of combinatorial optimization games, Math. Oper. Res., 1999.]; even when the core is nonempty, the core membership problem is intractable in general [Biro et al., The stable fixtures problem with payments, Games Econ. Behav., 2018]. Thus we study approximate core allocations for the multiple partners matching game, and provide an LPbased mechanism guaranteeing that no coalition is paid less than $2/3$ times the profit it makes on its own. Moreover, we show that the factor $2/3$ is best possible in general, but can be improved depending on how severely constrained the players are. Our result generalizes the recent work of Vazirani [Vazirani, The general graph matching game: approximate core, arXiv, 2021] from matching games to multiple partners matching games. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.01442&r= 
By:  Mohammad Rasouli; Michael I. Jordan 
Abstract:  With the growing use of distributed machine learning techniques, there is a growing need for data markets that allows agents to share data with each other. Nevertheless data has unique features that separates it from other commodities including replicability, cost of sharing, and ability to distort. We study a setup where each agent can be both buyer and seller of data. For this setup, we consider two cases: bilateral data exchange (trading data with data) and unilateral data exchange (trading data with money). We model bilateral sharing as a network formation game and show the existence of strongly stable outcome under the top agents property by allowing limited complementarity. We propose ordered match algorithm which can find the stable outcome in O(N^2) (N is the number of agents). For the unilateral sharing, under the assumption of additive cost structure, we construct competitive prices that can implement any social welfare maximizing outcome. Finally for this setup when agents have private information, we propose mixedVCG mechanism which uses zero cost data distortion of data sharing with its isolated impact to achieve budget balance while truthfully implementing socially optimal outcomes to the exact level of budget imbalance of standard VCG mechanisms. MixedVCG uses data distortions as data money for this purpose. We further relax zero cost data distortion assumption by proposing distortedmixedVCG. We also extend our model and results to data sharing via incremental inquiries and differential privacy costs. 
Date:  2021–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2107.08630&r= 