nep-des New Economics Papers
on Economic Design
Issue of 2021‒05‒24
twenty-two papers chosen by
Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford

  1. On the set of many-to-one strongly stable fractional matchings By Pablo Neme; Jorge Oviedo
  2. Marriage market with indifferences: A linear programming approach By Noelia Juárez; Pablo Neme; Jorge Oviedo
  3. Non-convergence to stability in coalition formation games By Agustín G. Bonifacio; Elena Inarra; Pablo Neme
  4. Serial Rules in a Multi-Unit Shapley-Scarf Market By Péter Biró; Flip Klijn; Szilvia Pápai
  5. Lattice structure of the random stable set in many-to-many matching markets By Noelia Juárez; Pablo Neme; Jorge Oviedo
  6. Arrovian Efficiency and Auditability in the Allocation of Discrete Resources By Pycia, Marek; Ünver, M. Utku
  7. Foundations of pseudomarkets: Walrasian equilibria for discrete resources By Antonio Miralles; Marek Pycia
  8. Committee Search Design By Christina Luxen; Tobias Rachidi
  9. Calibrated Click-Through Auctions: An Information Design Approach By Dirk Bergemann; Paul Duetting; Renato Paes Leme; Song Zuo
  10. Auctioning Annuities By Gaurab Aryal; Eduardo Fajnzylber; Maria F. Gabrielli; Manuel Willington
  11. CCP Auction Design By Wenqian Huang; Haoxiang Zhu
  12. Assessment of collusion damages in first price auctions By María Florencia Gabrielli; Manuel Willington
  13. All-Pay Matching Contests By Sela, Aner
  14. Individually Rational Rules for the Division Problem when the Number of Units to be Allotted is Endogenous By Gustavo Bergantiños; Jordi Massó; Alejandro Neme
  15. On the Decomposability of Fractional Allocations By Chatterji, Shurojit; Liu, Peng
  16. Competitive Gerrymandering and the Popular Vote By Bierbrauer, Felix; Polborn, Mattias
  17. Pairwise Justifiable Changes in Collective Choices By Salvador Barberà; Dolors Berga; Bernardo Moreno; Antonio Nicolò
  18. Task Allocation and On-the-job Training By Baccara, Mariagiovanna; Lee, SangMok; Yariv, Leeat
  19. Collective Information Acquisition By Eilat, Ran; Eliaz, Kfir
  20. Appointed Learning for the Common Good: Optimal Committee Size and Efficient Rewards By Gersbach, Hans; Mamageishvili, Akaki; Tejada, Oriol
  21. Dynamic Matching under Spatial Frictions By Yash Kanoria
  22. When to sell an indivisible object: Optimal timing with Markovian consumers By Kiho Yoon

  1. By: Pablo Neme (Universidad Nacional de San Luis/CONICET); Jorge Oviedo (Universidad Nacional de San Luis/CONICET)
    Abstract: For a many-to-one matching market where firms have strict and q-responsive preferences, we give a characterization of the set of strongly stable fractional match- ings as the union of the convex hull of all connected sets of stable matchings. We also prove that a strongly stable fractional matching is represented as a convex combination of stable matchings that are ordered in the common preferences of all firms.
    Keywords: Matching Markets Many-to-one Matching Market Strongly Stable Fractional Matchings Linear Programming
    Date: 2020–08
  2. By: Noelia Juárez (Universidad Nacional de San Luis/CONICET); Pablo Neme (Universidad Nacional de San Luis/CONICET); Jorge Oviedo (Universidad Nacional de San Luis/CONICET)
    Abstract: We study stable ans strongly stable matchings in the marriage market with indifference in their preferences. We characterize the stable matchings as integer extreme points of a convex polytope. We give an alternative proof for the integrity of the strongly stable matching polytope. Also, we compute men-optimal (women-optimal)stable and strongly stable matchings using linear programming. When preferences are strict we find the men- optimal (women-optimal) stable matching.
    Keywords: Matching markets The marriage market with indifferences Optimal Stable matchings Linear programming
    Date: 2020–08
  3. By: Agustín G. Bonifacio (Universidad Nacional de San Luis/CONICET); Elena Inarra (University of the Basque Country); Pablo Neme (Universidad Nacional de San Luis/CONICET)
    Abstract: We study the problem of convergence to stability in coalition formation games in which the strategies of each agent are coalitions in which she/he can partici- pate and outcomes are coalition structures. Given a natural blocking dynamic, an absorbing set is a minimum set of coalition structures that once reached is never abandoned. The coexistence of single and non-single absorbing sets is what causes lack of convergence to stability. To characterize games in which both types of set are present, we first relate circularity among coalitions in preferences (rings) with circularity among coalition structures (cycles) and show that there is a ring in pref- erences if and only if there is a cycle in coalition structures. Then we identify a special configuration of overlapping rings in preferences characterizing games that lack convergence to stability. Finally, we apply our findings to the study of games induced by sharing rules.
    Keywords: Coalition formation Matching markets Absorbing sets Convergence to stability
    JEL: C71 C78
    Date: 2020–09
  4. By: Péter Biró; Flip Klijn; Szilvia Pápai
    Abstract: We study generalized Shapley-Scarf exchange markets where each agent is endowed with multiple units of an indivisible and agent-specific good and monetary compensations are not possible. An outcome is given by a circulation which consists of a balanced exchange of goods. We focus on circulation rules that only require as input ordinal preference rankings of individual goods, and agents are assumed to have responsive preferences over bundles of goods. We study the properties of serial dictatorship rules which allow agents to choose either a single good or an entire bundle sequentially, according to a fixed ordering of the agents. We also introduce and explore extensions of these serial dictatorship rules that ensure individual rationality. The paper analyzes the normative and incentive properties of these four families of serial dictatorships and also shows that the individually rational extensions can be implemented with efficient graph algorithms.
    Keywords: indivisible goods, circulation, Shapley-Scarf market, serial dictatorship, effciency
    JEL: C72 C78 D61
    Date: 2021–05
  5. By: Noelia Juárez (Universidad Nacional de San Luis/CONICET); Pablo Neme (Universidad Nacional de San Luis/CONICET); Jorge Oviedo (Universidad Nacional de San Luis/CONICET)
    Abstract: We study the lattice structure of the set of random stable matchings for a many- to-many matching market. We define a partial order on the random stable set and present two natural binary operations for computing the least upper bound and the greatest lower bound for each side of the matching market. Then we prove that with these binary operations the set of random stable matchings forms two distributive lattices for the appropriate partial order, one for each side of the mar- ket. Moreover, these lattices are dual.
    Keywords: Lattice Structure Random Stable Matching markets Many-to-many Matching Markets
    JEL: C71 C78 D49
    Date: 2020–08
  6. By: Pycia, Marek; Ünver, M. Utku
    Abstract: In environments where heterogeneous indivisible resources are being allocated without monetary transfers and each agent has a unit demand, we show that an allocation mechanism is individually strategy-proof and Arrovian efficient, i.e., it always selects the best outcome with respect to some Arrovian social welfare function if, and only if, the mechanism is group strategy-proof and Pareto efficient. Re-interpreting Arrow's Independence of Irrelevant Alternatives in terms of auditability of the mechanism, we further show that these are precisely the mechanisms that are strategy-proof, Pareto efficient, and auditable.
    JEL: C78 D78
    Date: 2020–10
  7. By: Antonio Miralles; Marek Pycia
    Abstract: We study the assignment of discrete resources in a general model encompassing a wide range of applied environments, such as school choice, course allocation, and refugee resettlement. We allow single-unit and general multi-unit demands and any linear constraints. We prove the Second Welfare Theorem for these environments and a strong version of the First Welfare Theorem. In this way, we establish an equivalence between strong efficiency and decentralization through prices in discrete environments. Showing that all strongly efficient outcomes can be implemented through pseudomarkets, we provide a foundation for using pseudomarkets in market design.
    Keywords: Walrasian equilibrium, pseudomarkets, market design, revelation principle, welfare theorems, equilibrium existence, discrete markets, complementarities, constraints
    JEL: D47 D50
    Date: 2021–05
  8. By: Christina Luxen; Tobias Rachidi
    Abstract: This paper studies the design of committee search procedures. In each time period, a set of candidates of fixed size arrives, and committee members vote whether to accept a candidate out of this set or to continue costly search. We examine the implications of different sample sizes per period on acceptance standards and welfare, and we derive the welfare-maximizing number of candidates per period for small magnitudes of search costs. There is a trade-off between the expected value of a candidate conditional on stopping and the expected search costs. The resolution of this trade-off depends on the voting rule and the shape of the search cost function. In particular, we show that, for all cost functions and all qualified majority voting rules other than unanimity, welfare is increasing in the number of candidates per period if the magnitude of search costs is sufficiently small. This result stands in contrast to the classic finding for the single decision-maker case where the evaluation of multiple candidates per period does not improve welfare relative to reviewing one candidate at a time if there are no economies of scale in the simultaneous evaluation of multiple candidates.
    Keywords: Committee Search, Sequential Search, Multiple Options
    JEL: D71 D83
    Date: 2021–05
  9. By: Dirk Bergemann; Paul Duetting; Renato Paes Leme; Song Zuo
    Abstract: We analyze the optimal information design in a click-through auction with fixed valuations per click, but stochastic click-through rates. While the auctioneer takes as given the auction rule of the click-through auction, namely the generalized second-price auction, the auctioneer can design the information flow regarding the click-through rates among the bidders. A natural requirement in this context is to ask for the information structure to be calibrated in the learning sense. With this constraint, the auction needs to rank the ads by a product of the bid and an unbiased estimator of the click-through rates, and the task of designing an optimal information structure is thus reduced to the task of designing an optimal unbiased estimator. We show that in a symmetric setting with uncertainty about the click-through rates, the optimal information structure attains both social efficiency and surplus extraction. The optimal information structure requires private (rather than public) signals to the bidders. It also requires correlated (rather than independent) signals, even when the underlying uncertainty regarding the click-through rates is independent. Beyond symmetric settings, we show that the optimal information structure requires partial information disclosure.
    Date: 2021–05
  10. By: Gaurab Aryal (University of Virginia); Eduardo Fajnzylber (Universidad Adolfo Ibáñez); Maria F. Gabrielli (Universidad del Desarrollo/CONICET); Manuel Willington (Universidad Adolfo Ibáñez)
    Abstract: We use data on annuities to study and evaluate an imperfectly competitive market where firms have private information about their (annuitization) costs. Our data is from Chile, where the market is structured as first-price-auction-followed-by-bargaining, and where each retiree chooses a firm and an annuity contract to maximize her expected present discounted utility. We find that retirees with low savings have the highest in- formation processing cost, and they also care about firms' risk-ratings the most. Furthermore, while almost 50% of retirees reveal that they do not value leaving bequests, the rest have heterogeneous preference for bequest that, on average, increases with their savings. On the supply side, we find that firms' annuitization costs vary across retirees, and the average costs increase with retirees’ savings. If these costs were commonly known then the pensions would increase for everyone, but the increment would be substantial only for the high savers. Likewise, if we simplify the current pricing mechanism by implementing English auctions and "shutting down" the risk-ratings, then the pensions would increase, but again, mostly for the high savers.
    Keywords: Annuity Auctions Mortality Annuitization Costs
    JEL: D14 D44 D91 C57 J26 L13
    Date: 2020–11
  11. By: Wenqian Huang; Haoxiang Zhu
    Abstract: Central counterparties (CCPs) are systemically important. When a clearing member defaults, the CCP sells the defaulted portfolio to surviving members in an auction, and losses, if any, are partly absorbed by a cash pool prefunded by the surviving members. We propose a tractable auction model that incorporates this salient feature. We find that "juniorization" – the CCP first uses prefunded cash of members who submit bad bids – increases the auction price. Aggressive juniorization can push the auction price above the fair value and almost eliminate the need to use prefunded resources. Nonetheless, juniorization generates heterogeneous impact on members of different sizes.
    Keywords: central counterparty (CCP), auction, default management
    JEL: D44 G01 G23
    Date: 2021–05
  12. By: María Florencia Gabrielli (CONICET. Universidad Nacional de Cuyo.); Manuel Willington (Universidad Adolfo Ibañez)
    Abstract: We propose a structural method for estimating the revenue losses associated with bidding rings in symmetric and asymmetric first-price auctions. It is based on the structural analysis of auction data and is consistent with antitrust damage assessment methodologies: we build a but-for (competitive) scenario and estimate the differences between the two scenarios. We show in a Monte Carlo exercise that our methodology performs very well in moderate size samples. We apply it to Ohio Milk Data Set analyzed by Porter and Zona [1999] and find that damages are around 7%. Damages can be assessed without any information about unaffectedmarkets.
    Keywords: Collusion First price auctions Damages
    JEL: C1 C4 C7 D44 L4
    Date: 2020–05
  13. By: Sela, Aner
    Abstract: We study two-sided matching contests with two sets, each of which includes two heterogeneous players with commonly known types. The agents in each set compete in all-pay contests where they simultaneously send their costly efforts, and then are either assortatively or disassortatively matched. We characterize the players' equilibrium efforts for a general value function that assigns values for both agents who are matched as a function of their types. We then analyze the cross-effects of the players' types on their expected payoffs as well as on their expected total effort. We show that although each player's value function increases (decreases) in the types of the players in the other set, his expected payoff does not necessarily increase (decrease) in these types. In addition, depending on the value function, each player's type might have either a positive or a negative marginal effect on the players' expected total effort.
    Date: 2020–09
  14. By: Gustavo Bergantiños (Universidade de Vigo); Jordi Massó (Universitat Autónoma de Barcelona. Barcelona Graduate School of Economics); Alejandro Neme (Instituto de Matemática Aplicada San Luis. Universidad Nacional de San Luis . CONICET.)
    Abstract: We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and eficient families of rules, whenever agents' preferences are symmetric single-peaked on the set of possible allotments. Rules in the two families are in addition envy-free, but they differ on wether envy-freeness is considered on losses or on awards. Our main result states that (i) the family of constrained equal losses rules coincides with the class of all individually rational and eficient rules that satisfy justified envy-freeness on losses and (ii) the family of constrained equal awards rules coincides with the class of all individually rational and eficient rules that satisfy envy-freeness on awards.
    Keywords: Division problem Single-peaked preferences Individual rationality Efficiency Strategy-proofness Envy-freeness
    JEL: D71
    Date: 2020–05
  15. By: Chatterji, Shurojit (School of Economics, Singapore Management University); Liu, Peng (East China Normal University)
    Abstract: A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.
    Keywords: Indivisibility; Fractional allocation; Decomposability; Maximum flow
    JEL: C78 D82
    Date: 2021–04–28
  16. By: Bierbrauer, Felix; Polborn, Mattias
    Abstract: Gerrymandering undermines representative democracy by creating many uncompetitive legislative districts, and generating the very real possibility that a party that wins a clear majority of the popular vote does not win a majority of districts. We present a new approach to the determination of electoral districts, taking a design perspective. Specifically, we develop a redistricting game between two parties who both seek an advantage in upcoming elections, and show that we can achieve two desirable properties: First, the overall election outcome corresponds to the popular vote. Second, most districts are competitive.
    Keywords: Gerrymandering; legislative elections; redistricting
    JEL: C72 D72
    Date: 2020–10
  17. By: Salvador Barberà; Dolors Berga; Bernardo Moreno; Antonio Nicolò
    Abstract: Consider the following principle regarding the performance of collective choice rules. "If a rule selects alternative x in situation 1, and alternative y in situation 2, there must be an alternative z, and some member of society whose appreciation of z relative to x has increased when going from situation 1 to situation 2." This principle requires a minimal justification for the fall of x in the consideration of society: someone must have decreased its appreciation relative to some other possible alternative. We study the consequences of imposing this requirement of pairwise justifiability on a large class of collective choice rules that includes social choice and social welfare functions as particular cases. When preference profiles are unrestricted, it implies dictatorship, and both Arrow's and the Gibbard-Satterthwaite theorems become corollaries of our general result. On appropriately restricted domains, pairwise justifiability, along with anonymity and neutrality, characterize Condorcet consistent rules, thus providing a foundation for the choice of the alternatives that win by majority over all others in pairwise comparisons, when they exist.
    Keywords: pairwise justifiability, preference reversal condition, collective choice rules, collective choice correspondences, Social choice functions, social welfare functions, Condorcet consistency, Arrow's theorem, Gibbard-Satterthwaite's theorem
    JEL: D70 D71 D78
    Date: 2021–05
  18. By: Baccara, Mariagiovanna; Lee, SangMok; Yariv, Leeat
    Abstract: We study dynamic task allocation when service providers' expertise evolves. Clients arrive sequentially seeking service. Seniors provide superior service but entail waiting in a queue, which progresses at a speed dependent on their volume. Juniors offer service without wait and become seniors with experience. We show that clients choose senior service too frequently, generating longer waits and little training relative to the social optimum. Welfare gains from centralization are greater for larger institutions, better training technologies, and lower waiting costs. Finally, monitoring the seniors' queue increases welfare but may decrease training. Methodologically, we explore a matching setting in which agents' types are endogenous, and illustrate the usefulness of queueing theory techniques.
    Keywords: Dynamic Matching; market design; Training by Doing
    JEL: C02 C61 C78 D02 J22 L23
    Date: 2020–10
  19. By: Eilat, Ran; Eliaz, Kfir
    Abstract: We consider the problem faced by a group of players who need to collectively decide what public signal to acquire, and how to share its cost, before voting on whether to take some action, when each player is privately informed about his state-dependent payoffs from the action. We characterize the welfare maximizing mechanism for information acquisition taking into account the subsequent voting game. We identify novel distortions that arise from the information asymmetry and from the fact that after observing the signal realization, the players vote independently of their actions in the mechanism.
    Keywords: collective decision-making; Information-design; Mechanism-Design; Public Good Provision; rational inattention
    Date: 2020–09
  20. By: Gersbach, Hans; Mamageishvili, Akaki; Tejada, Oriol
    Abstract: A population of identical individuals must choose one of two alternatives under uncertainty about what the right alternative is. Individuals can gather information of increasing accuracy at an increasing convex utility cost. For such a setup, we analyze how vote delegation to a committee and suitable monetary transfers for its members can ensure that high or optimal levels of information are (jointly) acquired. Our main insight is that to maximize the probability of choosing the right alternative committee size must be small, no matter whether information acquisition costs are private or not. Our analysis and results cover two polar cases--information costs are either private or public--and unravel both the potential and the limitations of monetary transfers in committee design.
    Keywords: Voting - Committee - Cost sharing - Information acquisition - Reward scheme - Monetary transfers - Majority rule
    JEL: C72 D71 D8
    Date: 2020–09
  21. By: Yash Kanoria
    Abstract: We consider demand and supply which arise i.i.d. uniformly in the unit hypercube [0,1]^d in d dimensions, and need to be matched with each other while minimizing the expected average distance between matched pairs (the "cost"). We characterize the scaling behavior of the achievable cost in three models as a function of the dimension d: (i) Static matching of N demand units with N+M supply units. (ii) A semi-dynamic model where N+M supply units are present beforehand and N demand units arrive sequentially and must be matched immediately. (iii) A fully dynamic model where there are always m supply units present in the system, one supply and one demand unit arrive in each period, and the demand must be matched immediately. We show that one can achieve nearly the same cost under the semi-dynamic model as under the static model, despite uncertainty about the future, and that, under these two models, d=1 is the only case where cost far exceeds distance to the nearest neighbor (which is \Theta(1/N^{1/d})) and where adding excess supply M substantially reduces cost (by smoothing stochastic fluctuations at larger spatial length scales). In the fully dynamic model, we show that, remarkably, for all d we can achieve a cost only slightly more than the optimistic distance to the nearest neighbor \Theta(1/m^{1/d}). Thus, excess supply m reduces cost in the fully dynamic model for all $d$ by reducing the distance to the nearest neighbor. This is a fundamentally different phenomenon than that seen in the other two models, where excess supply reduces cost while leaving the distance to the nearest neighbor unchanged, only for d=1. Our achievability results are based on analysis of a certain "Hierarchical Greedy" algorithm which separately handles stochastic fluctuations at different length scales.
    Date: 2021–05
  22. By: Kiho Yoon
    Abstract: We study the problem of when to sell an indivisible object. There is a monopolistic seller who owns an indivisible object and plans to sell it over a given span of time to the set of potential buyers whose valuations for the object evolve over time. We formulate the seller's problem as a dynamic mechanism design problem. We provide the procedure for finding the optimal solution and show how to check incentive compatibility. We also examine sufficient conditions for the optimality of myopic stopping rule and ex-post individual rationality. In addition, we present some comparative static results regarding the seller's revenue and the selling time.
    Date: 2021–05

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