nep-des New Economics Papers
on Economic Design
Issue of 2020‒07‒20
thirteen papers chosen by
Alex Teytelboym
University of Oxford

  1. Are simple mechanisms optimal when agents are unsophisticated? By Jiangtao Li; Piotr Dworczak
  2. On the Optimal Allocation of Prizes in Best-of-Three All-Pay Auctions By Sela, Aner
  3. Optimal Contest Design: A General Approach By Igor Letina; Shuo Liu; Nick Netzer
  4. Reverse Contests By Sela, Aner
  5. Which Random Matching Markets Exhibit a Stark Effect of Competition? By Yash Kanoria; Seungki Min; Pengyu Qian
  6. On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations By Dongshuang Hou; Aymeric Lardon; Hao Sun
  7. Equity Principles and Interpersonal Comparison of Well-being: Old and New Joint Characterizations of Generalized Leximin, Rank-dependent Utilitarian, and Leximin Rules By Sakamoto, Norihito
  8. Strategy-Proof Aggregation Rules in Median Join-Semilattices and Arrowian Social Welfare Functions By Ernesto Savaglio; Stefano Vannucci
  9. Representative Committees of Peers By Reshef Meir; Fedor Sandomirskiy; Moshe Tennenholtz
  10. Minority Protection in Voting Mechanisms - Experimental Evidence By Engelmann, Dirk; Grüner, Hans Peter; Hoffmann, Timo; Possajennikov, Alex
  11. What Happens when Separate and Unequal School Districts Merge? By Robert Aue; Thilo Klein; Josue Ortega
  12. Stable source connection and assignment problems as multi-period shortest path problems By Leanne Streekstra; Christian Trudeau
  13. An egalitarian approach for sharing the cost of a spanning tree By Giménez Gómez, José M. (José Manuel); Peris, Josep E.; Subiza, Begoña

  1. By: Jiangtao Li (National University of Singapore); Piotr Dworczak (Group for Research in Applied Economics (GRAPE); Northwestern University)
    Abstract: We study the design of mechanisms involving agents that have limited strategic sophistication. The literature has identified several notions of simple mechanisms in which agents can determine their optimal strategy even if they lack cognitive skills such as predicting other agents' strategies (strategy-proof mechanisms), contingent reasoning (obviously strategy-proof mechanisms), or foresight (strongly obviously strategy-proof mechanisms). We examine whether it is optimal for the mechanism designer who faces strategically unsophisticated agents to offer a mechanism from the corresponding class of simple mechanisms. We show that when the designer uses a mechanism that is not simple, while she loses the ability to predict play, she may nevertheless be better off no matter how agents resolve their strategic confusion.
    Keywords: Simple mechanisms, complex mechanisms, robust mechanism design, dominant-strategy mechanisms, obviously strategy-proof mechanisms, strongly obviously strategy-proof mechanisms
    JEL: D71 D82 D86
    Date: 2020
  2. By: Sela, Aner
    Abstract: We study best-of-three all-pay auctions with two players who compete in three stages with a single match per stage. The first player to win two matches wins the contest. We assume that a prize sum is given, and show that if players are symmetric, the allocation of prizes does not have any effect on the players' expected total effort. On the other hand, if players are asymmetric, in order to maximize the players' expected total effort, independent of the players' types, it is not optimal to allocate a single final prize to the winner. Instead, it is optimal to allocate intermediate prizes in the first stage or/and in the second stage in addition to the final prize. When the asymmetry of the players' types is sufficiently high, it is optimal to allocate intermediate prizes in both two first stages and a final prize to the winner.
    Date: 2020–02
  3. By: Igor Letina; Shuo Liu; Nick Netzer
    Abstract: We consider the design of contests for n agents when the principal can choose both the prize profile and the contest success function. Our framework includes Tullock contests, Lazear-Rosen tournaments and all-pay contests as special cases, among others. We show that the optimal contest has an intermediate degree of competitiveness in the contest success function, and a minimally competitive prize profile with n-1 identical prizes. The optimum can be achieved with a nested Tullock contest. We extend the model to allow for imperfect performance measurement and for heterogeneous agents. We relate our results to a recent literature which has asked similar questions but has typically focused on the design of either the prize profile or the contest success function.
    Keywords: contest design, optimal contests, tournaments
    JEL: D02 D82 M52
    Date: 2020–05
  4. By: Sela, Aner
    Abstract: We study two reverse contests, A and B, with two agents, each of whom has both a linear reward function that increases in the agent's effort and an effort constraint. However, since the effort (output) of the agents has a negative effect on society, if the agents' effort constraints are relatively high, the designer in reverse contest A imposes a punishment such that the agent with the highest effort who caused the greatest damage is punished. Conversely, if the agents' effort constraints are relatively low, in reverse contest B, the designer awards a prize to the agent with the lowest effort who caused the smallest damage. We analyze the behavior of both symmetric and asymmetric agents in both contests A and B. In equilibrium, independent of the levels of the agents' effort constraints, both agents are active and they have positive expected payoffs. Furthermore, the agents might have the same expected payoff regardless of their asymmetric values of the prize/punishment or their asymmetric effort constraints.
    Date: 2020–02
  5. By: Yash Kanoria; Seungki Min; Pengyu Qian
    Abstract: We revisit the popular random matching market model introduced by Knuth (1976) and Pittel (1989), and shown by Ashlagi, Kanoria and Leshno (2013) to exhibit a "stark effect of competition", i.e., with any difference in the number of agents on the two sides, the short side agents obtain substantially better outcomes. We generalize the model to allow "partially connected" markets with each agent having an average degree $d$ in a random (undirected) graph. Each agent has a (uniformly random) preference ranking over only their neighbors in the graph. We characterize stable matchings in large markets and find that the short side enjoys a significant advantage only for $d$ exceeding $\log^2 n$ where $n$ is the number of agents on one side: For moderately connected markets with $d=o(\log^2 n)$, we find that there is no stark effect of competition, with agents on both sides getting a $\sqrt{d}$-ranked partner on average. Notably, this regime extends far beyond the connectivity threshold of $d= \Theta(\log n)$. In contrast, for densely connected markets with $d = \omega(\log^2 n)$, we find that the short side agents get $\log n$-ranked partner on average, while the long side agents get a partner of (much larger) rank $d/\log n$ on average. Numerical simulations of our model confirm and sharpen our theoretical predictions. Since preference list lengths in most real-world matching markets are much below $\log^2 n$, our findings may help explain why available datasets do not exhibit a strong effect of competition.
    Date: 2020–06
  6. By: Dongshuang Hou (NPU - Northwestern Polytechnical University [Xi'an]); Aymeric Lardon (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon); Hao Sun (NPU - Northwestern Polytechnical University [Xi'an])
    Abstract: Two new notions of stability of coalitions, based on the idea of exclusion or integration of players depending on how they affect allocations, are introduced for cooperative transferable utility games. The first one, called internal stability, requires that no coalition member would find that her departure from the coalition would improve her allocation or those of all her partners. The second one, called external stability, requires that coalitions members do not wish to recruit a new partner willing to join the coalition, since her arrival would hurt some of them. As an application of these two notions, we study the stability of Group Purchasing Organizations using the Shapley value to allocate costs between buyers. Our main results suggest that, when all buyers are initially alone, while small buyers will form internally and externally stable Group Purchasing Organizations to benefit from the best price discount, big buyers will be mutually exclusive and may cooperate with only small buyers.
    Keywords: Internal and external stability,Group purchasing organization,Cost allocation,Shapley value
    Date: 2020
  7. By: Sakamoto, Norihito
    Abstract: This paper characterizes new efficient and equitable social welfare orderings when individual well-beings are fully interpersonal comparable. Previous studies show that social welfare orderings satisfying the axioms of strong Pareto, anonymity, separability, and minimal equity are either weak utilitarian or leximin rules. By dropping the separability axiom, this study shows that there are various classes of distribution-sensitive social welfare orderings. In fact, simply imposing rank-separability instead of separability enables a class of social welfare orderings satisfying the axioms of strong Pareto, anonymity, and Pigou-Dalton transfer equity to be a generalized leximin rule (a general distribution-sensitive rule including leximin, rank-dependent utilitarianism, and their lexicographic compositions). This result is proved by a simple method that is intuitive and easy to understand without the need for advanced mathematical techniques, such as functional analysis and the hyperplane separation theorem, which are often used in typical social choice analyses. Following this new proof, the mechanism by which a class of reasonable social welfare orderings satisfying separability is limited to weak utilitarian and leximin rules can be easily understood and proved. This study also shows the impossibility theorem between the axioms of equity and continuity. Based on the results of previous studies and this paper, theoretical relationships between interpersonal comparability of individual well-being and equality axioms are clarified. That is, if the interpersonal comparability of well-being is a cardinal unit or ratio one, then Paretian and anonymous social welfare orderings are limited to Kolm-Pollack or Atkinson social welfare functions. If it is the ordinal level comparability, the desirable rule must be leximin. If it is the cardinal full comparability, the generalized leximin should be used.
    Keywords: Social Welfare Ordering, Joint Characterization, Generalized Leximin
    JEL: D71 D81
    Date: 2020–04
  8. By: Ernesto Savaglio; Stefano Vannucci
    Abstract: Three characterizations of the whole class of strategyproof aggregation rules on rich domains of locally unimodal total preorders in Önite median join-semilattices are provided. In particular, it is shown that such class consists precisely of generalized weak consensus-sponsorship rules induced by certain families of order Ölters of the coalition poset. It follows that the co-majority rule and many other inclusive aggregation rules belong to that class. The co-majority rule for an odd number of agents is also characterized. The existence of strategy-proof anonymous neutral and unanimity-respecting social welfare functions which satisfy a suitably relaxed independence condition is shown to follow from our characterizations.
    JEL: D71
    Date: 2020–07
  9. By: Reshef Meir; Fedor Sandomirskiy; Moshe Tennenholtz
    Abstract: A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is proportional to the fraction of issues, where his preferences disagree with the decision. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee. We show that a k-sortition (a random committee of k voters with the majority vote within the committee) leads to an outcome within the factor 1+O(1/k) of the optimal social cost for any number of voters n, any number of issues $m$, and any preference profile. For a small number of issues m, the social cost can be made even closer to optimal by delegation procedures that weigh committee members according to their number of followers. However, for large m, we demonstrate that the k-sortition is the worst-case optimal rule within a broad family of committee-based rules that take into account metric information about the preference profile of the whole population.
    Date: 2020–06
  10. By: Engelmann, Dirk; Grüner, Hans Peter; Hoffmann, Timo; Possajennikov, Alex
    Abstract: Under simple majority voting an absolute majority of voters may choose policies that are harmful to minorities. It is the purpose of sub- and super-majority rules to protect legitimate minority interests. We study how voting rules are chosen under the veil of ignorance. In our experiment, individuals choose voting rules for given distributions of gains and losses that can arise from a policy, but before learning their own valuation of the policy. We find that subjects on average adjust the voting rule in line with the skewness of the distribution. As a result, a higher share of the achievable surplus can be extracted with the suggested rules than with exogenously given simple majority voting. The rule choices, however, imperfectly reflect the distributions of benefits and costs, in expectation leading to only 63% of the surplus being extracted. Both under-protection and over-protection of minorities contribute to the loss. Voting insincerely leads to a further surplus loss of 5-15%. We classify subjects according to their rule choices and show that most subjects' rule choices follow the incentives embedded in the distributions. For a few participants, however, this is not the case, which leads to a large part of the surplus loss.
    Date: 2020–02
  11. By: Robert Aue; Thilo Klein; Josue Ortega
    Abstract: We study the welfare effects of school district consolidation, i.e. the integration of disjoint school districts into a centralised clearinghouse. We show theoretically that, in the worst-case scenario, district consolidation may unambiguously reduce students' welfare, even if the student-optimal stable matching is consistently chosen. However, on average all students experience expected welfare gains from district consolidation, particularly those who belong to smaller and over-demanded districts. Using data from the Hungarian secondary school assignment mechanism, we compute the actual welfare gains from district consolidation in Budapest and compare these to our theoretical predictions. We empirically document substantial welfare gains from district consolidation for students, equivalent to attending a school five kilometres closer to the students' home addresses. As an important building block of our empirical strategy, we describe a method to consistently estimate students' preferences over schools and vice versa that does not fully assume that students report their preferences truthfully in the student-proposing deferred acceptance algorithm.
    Date: 2020–06
  12. By: Leanne Streekstra (Department of Business and Economics, University of Southern Denmark); Christian Trudeau (Department of Economics, University of Windsor)
    Abstract: We extend the familiar shortest path problem by supposing that agents have demands over multiple periods. This potentially allows agents to combine their paths if their demands are complementary; for instance if one agent only needs a connection to the source in the summer while the other requires it only in the winter. We show that the resulting cost sharing problem always has a non-empty core, regardless of the number of agents and periods, the cost structure or the demand profile. We then exploit the fact that the model encompasses many well-studied problems to obtain or reobtain non-vacuity results for the cores of source-connection problems, (m-sided) assignment problems and minimum coloring problems.
    Keywords: shortest path, demand over multiple periods, cooperative game, core, source-connection, assignment.
    JEL: C71 D63
    Date: 2020–07
  13. By: Giménez Gómez, José M. (José Manuel); Peris, Josep E.; Subiza, Begoña
    Abstract: A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source when they are located at different places; that is, to connect them with the minimum possible cost. This objective requires the cooperation of the involved individuals and, once an efficient network is selected, the question is how to fairly allocate the total cost among these agents. To answer this question the literature proposes several rules providing allocations that, generally, depend on all the possible connection costs, regardless of whether these connections have been used or not in order to build the efficient network. To this regard, our approach defines a simple way to allocate the optimal cost with two main criteria: (1) each individual only pays attention to a few connection costs (the total cost of the optimal network and the cost of connecting by himself to the source); and (2) an egalitarian criteria is used to share costs or benefits. Then, we observe that the spanning tree cost allocation can be turned into a claims problem and, by using claims rules, we define two egalitarian solutions so that the total cost is allocated trying to equalize either the payments in which agents incur, or the benefit that agents obtain throughout cooperation. Finally, by comparing both proposals with other solution concepts proposed in the literature, we select equalizing payments as much as possible and axiomatically analyze it, paying special attention to coalitional stability (core selection), a central property whenever cooperation is needed to carry out the project. As our initial proposal might propose allocations outside the core, we modify it to obtain a core selection and we obtain an alternative interpretation of the Folk solution. Keywords: Minimum cost spanning tree, Egalitarian, Cost sharing, Core. JEL classification: C71, D63, D71.
    Keywords: Jocs cooperatius, Economia del benestar, 33 - Economia,
    Date: 2019

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