nep-des New Economics Papers
on Economic Design
Issue of 2021‒09‒27
seven papers chosen by
Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford

  1. Dynamic assignment without money: Optimality of spot mechanisms By Julien Combe; Vladyslav Nora; Olivier Tercieux
  2. Constrained School Choice with Incomplete Information By Hugo Gimbert; Claire Mathieu; Simon Mauras
  3. Matching markets with middlemen under transferable utility By Ata Atay; Eric Bahel; Tam\'as Solymosi
  4. Auctioning with Strategically Reticent Bidders By Jibang Wu; Ashwinkumar Badanidiyuru; Haifeng Xu
  5. Selling Impressions: Efficiency vs. Competition By Dirk Bergemann; Tibor Heumann; Stephen Morris; Constantine Sorokin; Eyal Winter
  6. Equilibria in Matching Markets with Soft and Hard Liquidity Constraints By Herings, P. Jean-Jacques; Zhou, Yu
  7. Potentials and Solutions of Cooperative Games. By Masayuki Odora

  1. By: Julien Combe (CREST-Ecole polytechnique, France); Vladyslav Nora (Economics department, Nazarbayev University); Olivier Tercieux (Paris School of Economics ,France)
    Abstract: We study a large market model of dynamic matching with no monetary transfers and a continuum of agents. Time is discrete and horizon finite. Agents are in the market from the first date and, at each date, have to be assigned items (or bundles of items). When the social planner can only elicit ordinal preferences of agents over the sequences of items, we prove that, under a mild regularity assumption, incentive compatible and ordinally efficient allocation rules coincide with spot mechanisms. A spot mechanism specifies “virtual prices” for items at each date and, at the beginning of time, for each agent, randomly selects a budget of virtual money according to a (potentially non-uniform) distribution over [0,1]. Then, at each date, the agent is allocated the item of his choice among the affordable ones. Spot mechanisms impose a linear structure on prices and, perhaps surprisingly, our result shows that this linear structure is what is needed when one requires incentive compatibility and ordinal efficiency. When the social planner can elicit cardinal preferences, we prove that, under a similar regularity assumption, incentive compatible and Pareto efficient mechanisms coincide with a class of mechanisms we call Spot Menu of Random Budgets mechanisms. These mechanisms are similar to spot mechanisms except that, at the beginning of the time, each agent must pick a distribution in a menu. This distribution is used to initially draw the agent's budget of virtual money.
    Date: 2021–07–27
  2. By: Hugo Gimbert; Claire Mathieu; Simon Mauras
    Abstract: School choice is the two-sided matching market where students (on one side) are to be matched with schools (on the other side) based on their mutual preferences. The classical algorithm to solve this problem is the celebrated deferred acceptance procedure, proposed by Gale and Shapley. After both sides have revealed their mutual preferences, the algorithm computes an optimal stable matching. Most often in practice, notably when the process is implemented by a national clearinghouse and thousands of schools enter the market, there is a quota on the number of applications that a student can submit: students have to perform a partial revelation of their preferences, based on partial information on the market. We model this situation by drawing each student type from a publicly known distribution and study Nash equilibria of the corresponding Bayesian game. We focus on symmetric equilibria, in which all students play the same strategy. We show existence of these equilibria in the general case, and provide two algorithms to compute such equilibria under additional assumptions, including the case where schools have identical preferences over students.
    Date: 2021–09
  3. By: Ata Atay; Eric Bahel; Tam\'as Solymosi
    Abstract: This paper studies matching markets in the presence of middlemen. In our framework, a buyer-seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer-seller pairs. Direct trade between a buyer and a seller is costlier than a trade mediated by a middleman. For each such market, we examine an associated cooperative game with transferable utility. First, we show that an optimal matching for a matching market with middlemen can be obtained by considering the two-sided assignment market where each buyer-seller pair is allowed to use the mediation service of the middlemen free of charge and attain the maximum surplus. Second, we prove that the core of a matching market with middlemen is always non-empty. Third, we show the existence of a buyer-optimal core allocation and a seller-optimal core allocation. In general, the core does not exhibit a middleman-optimal matching. Finally, we establish the coincidence between the core and the set of competitive equilibrium payoff vectors.
    Date: 2021–09
  4. By: Jibang Wu; Ashwinkumar Badanidiyuru; Haifeng Xu
    Abstract: Classic mechanism design often assumes that a bidder's action is restricted to report a type or a signal, possibly untruthfully. In today's digital economy, bidders are holding increasing amount of private information about the auctioned items. And due to legal or ethical concerns, they would demand to reveal partial but truthful information, as opposed to report untrue signal or misinformation. To accommodate such bidder behaviors in auction design, we propose and study a novel mechanism design setup where each bidder holds two kinds of information: (1) private \emph{value type}, which can be misreported; (2) private \emph{information variable}, which the bidder may want to conceal or partially reveal, but importantly, \emph{not} to misreport. We show that in this new setup, it is still possible to design mechanisms that are both \emph{Incentive and Information Compatible} (IIC). We develop two different black-box transformations, which convert any mechanism $\mathcal{M}$ for classic bidders to a mechanism $\mathcal{M}'$ for strategically reticent bidders, based on either outcome of expectation or expectation of outcome, respectively. We identify properties of the original mechanism $\mathcal{M}$ under which the transformation leads to IIC mechanisms $\mathcal{M}'$. Interestingly, as corollaries of these results, we show that running VCG with expected bidder values maximizes welfare whereas the mechanism using expected outcome of Myerson's auction maximizes revenue. Finally, we study how regulation on the auctioneer's usage of information may lead to more robust mechanisms.
    Date: 2021–09
  5. By: Dirk Bergemann (Cowles Foundation, Yale University); Tibor Heumann (Pontificia Universidad Católica de Chile); Stephen Morris (Dept. of Economics, MIT); Constantine Sorokin (Glasgow University and Higher School of Economics); Eyal Winter (The Hebrew University of Jerusalem)
    Abstract: In digital advertising, a publisher selling impressions faces a trade-off in deciding how precisely to match advertisers with viewers. A more precise match generates efficiency gains that the publisher can hope to exploit. A coarser match will generate a thicker market and thus more competition. The publisher can control the precision of the match by controlling the amount of information that advertisers have about viewers. We characterize the optimal trade-off when impressions are sold by auction. The publisher pools premium matches for advertisers (when there will be less competition on average) but gives advertisers full information about lower quality matches.
    Keywords: Second Price Auction, Conflation, Targeted Advertising, Impressions, Two-Sided Private Information, Bayesian Persuasion, Information Design
    JEL: D44 D47 D83 D84
    Date: 2021–08
  6. By: Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics); Zhou, Yu
    Abstract: We consider a matching with contracts model in the presence of liquidity constraints on the buyers side. Liquidity constraints can be either soft or hard. A convergent sequence of economies with increasingly stringent soft liquidity constraints is an economy with hard liquidity constraints at the limit. The limit of a corresponding convergent sequence of competitive equilibria may fail to be a competitive equilibrium in the limit economy. We establish limit results of two alternative notions of competitive equilibrium, quantity-constrained competitive equilibrium and expectational equilibrium, which do not suffer from such discontinuity problems. The implications of these limit results are discussed.
    JEL: C72 C78 D45 D52
    Date: 2021–09–20
  7. By: Masayuki Odora (Graduate School of Economics, Waseda University, 1-6-1, Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan.)
    Abstract: This study considers strategic communication before voting. Voters have partially conflicting interests rather than common interests. That is, voters cannot tell whether a collective decision is a matter of truth, such as guilty or innocent, or a matter of taste, such as left or right. A set of imperfectly informed voters communicates before casting their votes. From a statistical perspective, truth-telling by all voters in deliberation, coupled with majority rule, may lead to desirable outcomes asymptotically as the population of voters increases. Thus, from a statistical perspective, increasing the population of voters is desirable. This study, however, shows that truthful communication is not incentive-compatible with equilibrium behavior when the size of the electorate is sufficiently large. In particular, truthful communication by all voters is inconsistent with equilibrium for any voting rule and any degree of conflict when the population of voters becomes arbitrarily large. On the other hand, truthful communication might be an equilibrium for a small population of voters. Under these circumstances, voting rules matter. This study shows that majority rule most promotes truthful communication before voting.
    Keywords: Information aggregation, Common value elections, Private value elections, Deliberation, Voting rule, Conflicting interests
    JEL: C72 D71 D72
    Date: 2021–09

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