nep-des New Economics Papers
on Economic Design
Issue of 2021‒04‒26
eleven papers chosen by
Alex Teytelboym
University of Oxford

  1. Mechanism Design Approach to School Choice: One versus Many By Battal Dogan
  2. Matchings under Stability, Minimum Regret, and Forced and Forbidden Pairs in Marriage Problem By Mandal, Pinaki; Roy, Souvik
  3. I Want to Tell You? Maximizing Revenue in First-Price Two-Stage Auctions By Galit Ashkenazi-Golan; Yevgeny Tsodikovich; Yannick Viossat
  4. New axioms for top trading cycles By Siwei Chen; Yajing Chen; Chia-Ling Hsu
  5. Singles monotonicity and stability in one-to-one matching problems By Yoichi Kasajima; Manabu Toda
  6. The probabilistic rank random assignment rule and its axiomatic characterization By Yajing Chen; Patrick Harless; Zhenhua Jiao
  7. Monotonic Norms and Orthogonal Issues in Multidimensional Voting By Alex Gershkov; Benny Moldovanu; Xianwen Shi
  8. Worst Case in Voting and Bargaining By Anna Bogomolnaia; Ron Holzman; Hervé Moulin
  9. Voting Agendas and Preferences on Trees: Theory and Practice By Andreas Kleiner; Benny Moldovanu
  10. On the relation between Preference Reversal and Strategy-Proofness By K. P. S. Bhaskara Rao; Achille Basile; Surekha Rao
  11. Extreme Points and Majorization: Economic Applications By Andreas Kleiner; Benny Moldovanu; Philipp Strack

  1. By: Battal Dogan
    Abstract: A vast majority of the school choice literature focuses on designing mechanisms to simultaneously assign students to many schools, and employs a "make it up as you go along" approach when it comes to each school's admissions policy. An alternative approach is to focus on the admissions policy for one school. This is especially relevant for effectively communicating policy objectives such as achieving a diverse student body or implementing affirmative action. I argue that the latter approach is relatively under-examined and deserves more attention in the future.
    Date: 2021–04
  2. By: Mandal, Pinaki; Roy, Souvik
    Abstract: We provide a class of algorithms, called men-women proposing deferred acceptance (MWPDA) algorithms, that can produce all stable matchings at every preference profile for the marriage problem. Next, we provide an algorithm that produces a minimum regret stable matching at every preference profile. We also show that its outcome is always women-optimal in the set of all minimum regret stable matchings. Finally, we provide an algorithm that produces a stable matching with given sets of forced and forbidden pairs at every preference profile, whenever such a matching exists. As before, here too we show that the outcome of the said algorithm is women-optimal in the set of all stable matchings with given sets of forced and forbidden pairs.
    Keywords: Two-sided matching; Marriage problem; Pairwise stability; Stability; Minimum regret; Forced and forbidden pairs
    JEL: C78
    Date: 2021–04–18
  3. By: Galit Ashkenazi-Golan; Yevgeny Tsodikovich; Yannick Viossat
    Abstract: A common practice in many auctions is to offer bidders an opportunity to improve their bids, known as a Best and Final Offer (BAFO) stage. This final bid can depend on new information provided about either the asset or the competitors. This paper examines the effects of new information regarding competitors, seeking to determine what information the auctioneer should provide assuming the set of allowable bids is discrete. The rational strategy profile that maximizes the revenue of the auctioneer is the one where each bidder makes the highest possible bid that is lower than his valuation of the item. This strategy profile is an equilibrium for a large enough number of bidders, regardless of the information released. We compare the number of bidders needed for this profile to be an equilibrium under different information settings. We find that it becomes an equilibrium with fewer bidders when less additional information is made available to the bidders regarding the competition. It follows that when the number of bidders is a priori unknown, there are some advantages to the auctioneer to not reveal information.
    Date: 2021–04
  4. By: Siwei Chen; Yajing Chen; Chia-Ling Hsu
    Abstract: School choice is of great importance both in theory and practice. This paper studies the (student-optimal) top trading cycles mechanism (TTCM) in an axiomatic way. We introduce two new axioms: MBG (mutual best group)-quota-rationality and MBG-robust efficiency. While stability implies MBG-quota-rationality, MBG-robust efficiency is weaker than robust efficiency, which is stronger than the combination of efficiency and group strategy-proofness. The TTCM is characterized by MBG-quota-rationality and MBG-robust efficiency. Our results construct a new basis to compare the TTCM with the other school choice mechanisms, especially the student-optimal stable mechanism under Ergin but not Kesten-acyclic priority structures.
    Date: 2021–04
  5. By: Yoichi Kasajima (School of Social Sciences, Waseda University); Manabu Toda (School of Social Sciences, Waseda University)
    Abstract: We consider two-sided one-to-one matching problems (between men and women) and study a new requirement called “own-side singles monotonicity.” Suppose that there is an agent who is not matched in a problem. Suppose for simplicity it is a woman. Now in a new problem (with the same set of agents), we improve (or leave unchanged) her ranking for each agent on the opposite side of her. Own-side singles monotonicity requires that each agent on her side should not be made better off (except for her). Unfortunately, no single-valued solution satisfies own-side singles monotonicity and stability. However, there is a (multi-valued) solution, the stable solution, that does. We provide two characterizations of the stable solution based on this property. It is the unique solution satisfying weak unanimity, null player invariance, own-side singles monotonicity, and consistency. The uniqueness also holds by replacing consistency with Maskin invariance. In addition, we study the impact of improving her ranking on the welfare of the agents on the opposite side of her.
    Keywords: property regimes, one-to-one matching; own-side singles monotonicity; other-side singles monotonicity; stability; consistency; Maskin invariance.
    JEL: C71 C78 D47
  6. By: Yajing Chen; Patrick Harless; Zhenhua Jiao
    Abstract: This paper considers the problem of randomly assigning a set of objects to a set of agents based on the ordinal preferences of agents. We generalize the well-known immediate acceptance algorithm to the afore-mentioned random environments and define the probabilistic rank rule (PR rule). We introduce two new axioms: sd-rank-fairness, and equal-rank envy-freeness. Sd-rank-fairness implies sd-efficiency. Equal-rank envy-freeness implies equal treatment of equals. Sd-rank-fairness and equal-rank envy-freeness are enough to characterize the PR rule.
    Date: 2021–04
  7. By: Alex Gershkov; Benny Moldovanu; Xianwen Shi
    Abstract: We study issue-by-issue voting by majority and incentive compatibility in multi- dimensional frameworks where privately informed agents have preferences induced by general norms and where dimensions are endogenously chosen. We uncover the deep connections between dominant strategy incentive compatibility (DIC) on the one hand, and several geometric/functional analytic concepts on the other. Our main results are: 1) Marginal medians are DIC if and only if they are calculated with respect to coor- dinates de ned by a basis such that the norm is orthant-monotonic in the associated coordinate system. 2) Equivalently, marginal medians are DIC if and only if they are computed with respect to a basis such that, for any vector in the basis, any linear combination of the other vectors is Birkho¤-James orthogonal to it. 3) We show how semi-inner products and normality provide an analytic method that can be used to nd all DIC marginal medians. 4) As an application, we derive all DIC marginal medians for lp spaces of any nite dimension, and show that they do not depend on p (unless p = 2).
    JEL: D71 D82
    Date: 2021–04
  8. By: Anna Bogomolnaia (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Glasgow, HSE St Petersburg - Higher School of Economics - St Petersburg); Ron Holzman (Technion - Israel Institute of Technology [Haifa]); Hervé Moulin (University of Glasgow, HSE St Petersburg - Higher School of Economics - St Petersburg)
    Abstract: The guarantee of an anonymous mechanism is the worst case welfare an agent can secure against unanimously adversarial others. How high can such a guarantee be, and what type of mechanism achieves it?. We address the worst case design question in the n-person probabilistic voting/bargaining model with p deterministic outcomes. If n superior or equal to p the uniform lottery is the only maximal (unimprovable) guarantee; there are many more if p>n, in particular the ones inspired by the random dictator mechanism and by voting by veto. If n=2 the maximal set M(n,p) is a simple polytope where each vertex combines a round of vetoes with one of random dictatorship. For p>n superior or egal to 3, writing d=[((p-1)/n)], we show that the duak veto and random dictator guarantees, together with the uniform one, are the building blocks of 2^{d} simplices of dimension d in M(n,p). Their vertices are guarantees easy to interpret and implement. The set M(n,p) may contain other guarantees as well; what we can say in full generality is that it is a finite union of polytopes, all sharing the uniform guarantee.
    Keywords: worst case,guarantees,voting by veto,random dictator
    Date: 2021–04
  9. By: Andreas Kleiner; Benny Moldovanu
    Abstract: We study how parliaments and committees select one out of several alternatives when options cannot be ordered along a "left-right" axis. Which voting agendas are used in practice, and how should they be designed? We assume preferences are single-peaked on a tree and study convex agendas where, at each stage in the voting process, the tree of remaining alternatives is divided into two subtrees that are subjected to a Yes-No vote. We show that strategic voting coincides with sincere, unsophisticated voting. Based on inference results and revealed preference arguments, we illustrate the empirical implications for two case studies.
    JEL: D71 D72
    Date: 2021–04
  10. By: K. P. S. Bhaskara Rao; Achille Basile; Surekha Rao
    Abstract: We analyze the relation between strategy-proofness and preference reversal in the case that agents may declare indifference. Interestingly, Berga and Moreno (2020), have recently derived preference reversal from group strategy-proofness of social choice functions on strict preferences domains if the range has no more than three elements. We extend this result and at the same time simplify it. Our analysis points out the role of individual strategy-proofness in deriving the preference reversal property, giving back to the latter its original individual nature (cfr. Eliaz, 2004). Moreover, we show that the difficulties Berga and Moreno highlighted relaxing the assumption on the cardinality of the range, disappear under a proper assumption on the domain. We introduce the concept of complete sets of preferences and show that individual strategy-proofness is sufficient to obtain the preference reversal property when the agents' feasible set of orderings is complete. This covers interesting cases like single peaked preferences, rich domains admitting regular social choice functions, and universal domains. The fact that we use individual rather than group strategy-proofness, allows to get immediately some of the known, and some new, equivalences between individual and group strategy-proofness. Finally, we show that group strategy-proofness is only really needed to obtain preference reversal if there are infinitely many voters.
    Date: 2021–04
  11. By: Andreas Kleiner; Benny Moldovanu; Philipp Strack
    Abstract: We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.
    JEL: D81 D82
    Date: 2021–04

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