nep-des New Economics Papers
on Economic Design
Issue of 2020‒10‒19
seven papers chosen by
Alex Teytelboym
University of Oxford

  1. Dynamic Reserves in Matching Markets By Aygün, Orhan; Turhan, Bertan
  2. Slot-specific Priorities with Capacity Transfers By Avataneo, Michelle; Turhan, Bertan
  3. Assignment Maximization By Afacan, Mustafa Oguz; Bó, Inácio; Turhan, Bertan
  4. On the Revealed Preference Analysis of Stable Aggregate Matchings By Thomas Demuynck; Umutcan Salman
  5. Ordinal Bayesian incentive compatibility in random assignment model By Sulagna Dasgupta; Debasis Mishra
  6. Majority properties of positional social preference correspondences By Mostapha Diss; Michele Gori
  7. On the axiomatic approach to sharing the revenues from broadcasting sports leagues By Bergantiños, Gustavo; Moreno-Ternero, Juan D.

  1. By: Aygün, Orhan; Turhan, Bertan
    Abstract: We study a school choice problem under affirmative action policies where authorities reserve a certain fraction of the slots at each school for specific student groups, and where students have preferences not only over the schools they are matched to but also the type of slots they receive. Such reservation policies might cause waste in instances of low student demand from some student groups. To propose a solution to this issue, we construct a family of choice functions, dynamic reserves choice functions, for schools that respect within-group fairness and allow the transfer of otherwise vacant slots from low-demand groups to high-demand groups. We propose the cumulative offer mechanism (COM) as an allocation rule where each school uses a dynamic reserves choice function and show that it is stable with respect to schools’ choice functions, is strategy-proof, and respects improvements. Furthermore, we show that transferring more of the otherwise vacant slots leads to strategy-proof Pareto improvement under the COM.
    Date: 2019–09–25
  2. By: Avataneo, Michelle; Turhan, Bertan
    Abstract: In many real-world matching applications, there are restrictions for institutions either on priorities of their slots or on the transferability of unfilled slots over others (or both). Motivated by the need in such real-life matching problems, this paper formulates a family of practical choice rules, slot-specific priorities with capacity transfers (SSPwCT). These practical rules invoke both slot-specific priorities structure and transferability of vacant slots. We show that the cumulative offer mechanism (COM) is stable, strategy-proof and respects improvements with regards to SSPwCT choice rules. Transferring the capacity of one more unfilled slot, while all else is constant, leads to strategy-proof Pareto improvement of the COM. Following Kominer’ s (2020) formulation, we also provide comparative static results for expansion of branch capacity and addition of new contracts in the SSPwCT framework. Our results have implications for resource allocation problems with diversity considerations.
    Date: 2020–09–01
  3. By: Afacan, Mustafa Oguz; Bó, Inácio; Turhan, Bertan
    Abstract: We evaluate the goal of maximizing the number of individuals matched to acceptable outcomes. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated, in terms of number of assignments, in equilibrium. The second are fair for unassigned students and assign weakly more students than stable mechanisms in equilibrium. We provide comparisons with well-known mechanisms through computer simulations. Those show that the difference in number of matched agents between the proposed mechanisms and others in the literature is large and significant.
    Date: 2020–01–09
  4. By: Thomas Demuynck; Umutcan Salman
    Abstract: We extend the analysis of (Echenique, Lee, Shum, and Yenmez, 2013) by looking at the testable revealed preference restrictions for stable aggregate matchings with non-transferable utility. We rephrase their revealed preference test in terms of a bipartite graph. From this, we obtain an simple condition that verifies whether a given matching is rationalisable. Next, for a matching that is not rationalisable, we show how to find the minimal number of matches that needs to be removed in order to restore rationalisability. This produces a goodness-of-fit measure that indicates how close a matching is to being rationalisable. We also show that the related problem of finding the minimal number of types that we need to remove in order to obtain rationalisability is NP-hard. We provide two illustrations to demonstrate the usefulness of our results.
    Keywords: Revealed preference theory; com- putational complexity; stability; two-sided matching markets
    JEL: C78 D11
    Date: 2020–09
  5. By: Sulagna Dasgupta; Debasis Mishra
    Abstract: We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is a uniform prior, then a large class of random mechanisms are OBIC with respect to this prior -- this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent priors in some neighborhood of a given independent prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.
    Date: 2020–09
  6. By: Mostapha Diss (CRESE, Univ. Bourgogne Franche-Comté); Michele Gori (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze)
    Abstract: We characterize the positional social preference correspondences (spc) satisfying the qualified majority property for any given majority threshold. We also characterize the positional spcs satisfying the minimal majority property. We next evaluate the probability that the Borda, the Plurality and the Antiplurality spcs fulfil the two aforementioned properties under two assumptions on individuals’ preferences in the presence of three and four alternatives for various sizes of the society. Our results show that the Borda spc is the positional spc which better behaves in relation with the qualified majority principle and the minimal majority principle. Finally, we propose some remarks on the concept of Condorcet consistency for social choice correspondences.
    Keywords: social preference correspondence, social choice correspondence, positional rule, qualified majority, probability, Condorcet consistency.
    JEL: D71
    Date: 2020–07
  7. By: Bergantiños, Gustavo; Moreno-Ternero, Juan D.
    Abstract: We take the axiomatic approach to uncover the structure of the revenue-sharing problem from broadcasting sports leagues. Our starting point is to explore the implications of three basic axioms: additivity, order preservation and weak upper bound. We show that the combination of these axioms characterizes a large family of rules, which is made of compromises between the uniform rule and concede-and-divide, such as the one represented by the equal-split rule. The members of the family are fully ranked according to the Lorenz dominance criterion, and the structure of the family guarantees the existence of a majority voting equilibrium. Strengthening some of the previous axioms, or adding new ones, we provide additional characterizations within the family. Weakening some of those axioms, we also characterize several families encompassing the original one.
    Keywords: resource allocation, broadcasting, sport leagues, axioms, concede-and-divide.
    JEL: C71
    Date: 2020–09–28

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