nep-des New Economics Papers
on Economic Design
Issue of 2021‒07‒19
nine papers chosen by
Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford

  1. Minimal-Access Rights in School Choice and the Deferred Acceptance Mechanism By Bettina Klaus; Flip Klijn
  2. On the Impact of Information Acquisition and Aftermarkets on Auction Efficiency By Moshe Babaioff; Nicole Immorlica; Yingkai Li; Brendan Lucier
  3. Farsighted Objections and Maximality in One-to-one Matching Problems By Kimya, Mert
  4. Reduced-Form Allocations for Multiple Indivisible Objects under Constraints By Xu Lang; Zaifu Yang
  5. Coalition Formation Under Dominance Invariance By Kimya, Mert
  6. Smart Matching Platforms and Heterogeneous Beliefs in Centralized School Choice By Felipe Arteaga; Adam J. Kapor; Christopher A. Neilson; Seth D. Zimmerman
  7. Mechanism Design for Efficient Nash Equilibrium in Oligopolistic Markets By Kaiying Lin; Beibei Wang; Pengcheng You
  8. Information Aggregation with Delegation of Votes By Dhillon, Amrita; Kotsialou, Grammateia; Xefteris, Dimitris
  9. Collective Choice with Heterogeneous Time Preferences By Mikhail Pakhnin

  1. By: Bettina Klaus; Flip Klijn
    Abstract: A classical school choice problem consists of a set of schools with priorities over students and a set of students with preferences over schools. Schools' priorities are often based on multiple criteria, e.g., merit-based test scores as well as minimal-access rights (siblings attending the school, students' proximity to the school, etc.). Traditionally, minimal-access rights are incorporated into priorities by always giving minimal-access students higher priority over non-minimal-access students. However, stability based on such adjusted priorities can be considered unfair because a minimal-access student may be admitted to a popular school while another student with higher merit-score but without minimal-access right is rejected, even though the former minimal-access student could easily attend another of her minimal-access schools. We therefore weaken stability to minimal-access stability: minimal-access rights only promote access to at most one minimal-access school. Apart from minimal-access stability, we also would want a school choice mechanism to satisfy strategy-proofness and minimal-access monotonicity, i.e., additional minimal-access rights for a student do not harm her. Our main result is that the student-proposing deferred acceptance mechanism is the only mechanism that satisfies minimal-access stability, strategy-proofness, and minimal-access monotonicity. Since this mechanism is in fact stable, our result can be interpreted as an impossibility result: fairer outcomes that are made possible by the weaker property of minimal-access stability are incompatible with strategy-proofness and minimal-access monotonicity.
    Keywords: school choice, priorities, minimal-access rights, justified envy, stability, deferred acceptance
    JEL: C78 D47 D63 D78
    Date: 2021–06
  2. By: Moshe Babaioff; Nicole Immorlica; Yingkai Li; Brendan Lucier
    Abstract: A common assumption in auction theory is that the information available to the agents is given exogenously and that the auctioneer has full control over the market. In practice, agents might be able to acquire information about their competitors before the auction (by exerting some costly effort), and might be able to resell acquired items in an aftermarket. The auctioneer has no control over those aspects, yet their existence influences agents' strategic behavior and the overall equilibrium welfare can strictly decrease as a result. We show that if an auction is smooth (e.g., first-price auction, all-pay auction), then the corresponding price of anarchy bound due to smoothness continues to hold in any environment with (a) information acquisition on opponents' valuations, and/or (b) an aftermarket satisfying two mild conditions (voluntary participation and weak budget balance). We also consider the special case with two ex ante symmetric bidders, where the first-price auction is known to be efficient in isolation. We show that information acquisition can lead to efficiency loss in this environment, but aftermarkets do not: any equilibrium of a first-price or all-pay auction combined with an aftermarket is still efficient.
    Date: 2021–07
  3. By: Kimya, Mert
    Abstract: We characterize the set of stable matchings when individuals are farsighted and when they choose their objections optimally along a farsighted objection path. We use a solution concept called maximal farsighted set (MFS), which is an adaptation of the concepts developed in Dutta and Vohra (2017) and Dutta and Vartiainen (2020) to one-to-one matching problems. MFS always exists, but it need not be unique. There is a unique largest MFS that contains all other, which is equal to the largest consistent set of Chwe (1994). This implies that the largest consistent set embodies the idea of maximality in one-to-one matching problems.
    Date: 2020–09
  4. By: Xu Lang; Zaifu Yang
    Abstract: We examine the implementation of reduced-form allocation rules that assign multiple indivisible objects to many agents, with incomplete information and distributional constraints across objects and agents. To obtain implementability results, we adopt a lift-and-project approach, which reduces the problem to a problem of enumerating finite generators of a projection cone. We study geometric and combinatorial properties of the projection cone and provide a total unimodularity condition that leads to several characterization results including those on hierarchies and bihierarchies. Our results have applications in matching markets with constraints where agents may have ordinal or cardinal preferences.
    Keywords: Implementation, Reduced-form rules, Indivisible goods, Distributional constraints, Total unimodularity, Incomplete information.
    JEL: D44 C65
    Date: 2021–07
  5. By: Kimya, Mert
    Abstract: An abstract game satisfies Dominance Invariance if the indirect and the direct dominance relations, or myopic and farsighted dominance, are equivalent. Mauleon, Molis, Vannetelbosch, and Vergote (2014) study Dominance Invariance in match- ing problems as an attractive condition that eliminates the differences between a farsighted solution concept and its myopic counterpart. We show that Dominance Invariance can also be used to eliminate the differences between various farsighted solution concepts in any abstract game. Together with an additional condition called No Infinite Chains, Dominance Invariance implies the existence and unique- ness of the farsighted stable set, its equivalence to the largest consistent set and its equivalence to the (strong) rational expectations farsighted stable set when the latter exists. This also implies that both the farsighted stable set and the largest consistent set do not su er from the problem of maximality under these conditions.
    Keywords: Farsighted stability; Coalitional games; Farsighted stable set; Largest Consistent Set
    Date: 2021–06
  6. By: Felipe Arteaga; Adam J. Kapor; Christopher A. Neilson; Seth D. Zimmerman
    Abstract: Many school districts with centralized school choice adopt strategyproof assignment mechanisms to relieve applicants of the need to strategize on the basis of beliefs about their own admissions chances. This paper shows that beliefs about admissions chances shape choice outcomes even when the assignment mechanism is strategyproof by influencing the way applicants search for schools, and that “smart matching platforms” that provide live feedback on admissions chances help applicants search more effectively. Motivated by a model in which applicants engage in costly search for schools and over-optimism can lead to under-search, we use data from a large-scale survey of choice participants in Chile to show that learning about schools is hard, that beliefs about admissions chances guide the decision to stop searching, and that applicants systematically underestimate non-placement risk. We then use RCT and RD research designs to evaluate live feedback policies in the Chilean and New Haven choice systems. 22% of applicants submitting applications where risks of non-placement are high respond to warnings by adding schools to their lists, reducing non-placement risk by 58%. These results replicate across settings and over time. Reducing the strategic burden of school choice requires not just strategyproofness inside the centralized system, but also choice supports for the strategic decisions that inevitably remain outside of it.
    JEL: D83 H75 I2 J01
    Date: 2021–06
  7. By: Kaiying Lin; Beibei Wang; Pengcheng You
    Abstract: This paper investigates the efficiency loss in social cost caused by strategic bidding behavior of individual participants in a supply-demand balancing market, and proposes a mechanism to fully recover equilibrium social optimum via subsidization and taxation. We characterize the competition among supply-side firms to meet given inelastic demand, with linear supply function bidding and the proposed efficiency recovery mechanism. We show that the Nash equilibrium of such a game exists under mild conditions, and more importantly, it achieves the underlying efficient supply dispatch and the market clearing price that reflects the truthful system marginal production cost. Further, the mechanism can be tuned to guarantee self-sufficiency, i.e., taxes collected counterbalance subsidies needed. Extensive numerical case studies are run to validate the equilibrium analysis, and we employ individual net profit and a modified version of Lerner index as two metrics to evaluate the impact of the mechanism on market outcomes by varying its tuning parameter and firm heterogeneity.
    Date: 2021–06
  8. By: Dhillon, Amrita; Kotsialou, Grammateia; Xefteris, Dimitris
    Abstract: Recent developments in blockchain technology have made possible greater progress on secure electronic voting, opening the way to better ways of democratic decision making. In this paper we formalise the features of ``liquid democracy'' which allows voters to delegate their votes to other voters, and we explore whether it improves information aggregation as compared to direct voting. We consider a two-alternative setup with truth-seeking voters (informed and uninformed) and partisan ones (leftists and rightists), and we show that delegation improves information aggregation in finite elections. We also propose a mechanism that further improves the information aggregation properties of delegation in private information settings, by guaranteeing that all vote transfers are from uninformed to informed truth-seeking voters. Delegation offers effective ways for truth-seeking uninformed voters to boost the vote-share of the alternative that matches the state of the world in all considered setups and hence deserves policy makers' attention.
    Date: 2021–01–02
  9. By: Mikhail Pakhnin
    Abstract: This paper reviews recent research on the aggregation of heterogeneous time preferences. Main results are illustrated in simple Ramsey models with two or three agents who differ in their discount factors. We employ an intertemporal view on these models and argue that preferences of a decision maker should be represented by a sequence of utility functions. This allows us to clarify the issue of dynamic inconsistency and relate it to simple properties of discounting. We distinguish between private and common consumption cases. In the private consumption case, we discuss the properties of sequences of Paretian social welfare functions and explain why the notion of Pareto optimality under heterogeneous time preferences becomes problematic. In the common consumption case, we focus on the problem of collective choice under heterogeneous time preferences, discuss the difficulties with dynamic voting procedures and review some ways to overcome them. We conclude by highlighting the implications of our discussion for the problem of choosing an appropriate social discount rate.
    Keywords: collective decisions, social welfare function, heterogeneous agents, time consistency, voting, social discount rate
    JEL: D15 D71 H43 O40
    Date: 2021

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