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on Economic Design |
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Issue of 2021‒03‒01
eight papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Maximilian Mordig; Riccardo Della Vecchia; Nicol\`o Cesa-Bianchi; Bernhard Sch\"olkopf |
| Abstract: | We introduce a variant of the three-sided stable matching problem for a PhD market with students, advisors, and co-advisors. In our formalization, students have consistent (lexicographic) preferences over advisors and co-advisors, and the latter have preferences over students only (hence advisors and co-advisors are cooperative). A student must be matched to one advisor and one co-advisor, or not at all. In contrast to previous work, advisor-student and student-co-advisor pairs may not be mutually acceptable, e.g., a student may not want to work with an advisor or co-advisor and vice versa. We show that stable three-sided matchings always exist, and present the PhD algorithm, a three-sided matching algorithm with polynomial running time which uses any two-sided stable matching algorithm as matching engine. Borrowing from results on two-sided markets, we provide some approximate optimality results. We also present an extension to three-sided markets with quotas, where each student conducts several projects, and each project is supervised by one advisor and one co-advisor. As it is often the case in practice that the same student should not do more than one project with the same advisor or co-advisor, we modify our PhD algorithm for this setting by adapting the two-sided Gale--Shapley algorithm to many-to-many two-sided markets, in which the same pair can match at most once. We also generalize the three-sided market to an $n$-sided market consisting of $n-1$ two-sided markets. We extend the PhD algorithm to this multi-sided setting to compute a stable matching in polynomial time, and we discuss its extension to arbitrary quotas. Finally, we illustrate the challenges that arise when not all advisor-co-advisor pairs are compatible, and critically review the statements from [30, 29]. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.11834&r=all |
| By: | Alfred Galichon; Bernard Salani\'e |
| Abstract: | We investigate in this paper the theory and econometrics of optimal matchings with competing criteria. The surplus from a marriage match, for instance, may depend both on the incomes and on the educations of the partners, as well as on characteristics that the analyst does not observe. Even if the surplus is complementary in incomes, and complementary in educations, imperfect correlation between income and education at the individual level implies that the social optimum must trade off matching on incomes and matching on educations. Given a flexible specification of the surplus function, we characterize under mild assumptions the properties of the set of feasible matchings and of the socially optimal matching. Then we show how data on the covariation of the types of the partners in observed matches can be used to test that the observed matches are socially optimal for this specification, and to estimate the parameters that define social preferences over matches. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.12811&r=all |
| By: | Komal Malik (Indian Statistical Institute, Delhi); Kolagani Paramahamsa (Indian Statistical Institute, Delhi) |
| Abstract: | A seller is selling a pair of complementary goods to an agent. The agent consumes the goods only in a certain ratio and freely disposes of excess in either of the goods. The value of the bundle and the ratio are private information of the agent. In this two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price mechanism for a class of distributions; that is, it has a di↵erent posted price for each ratio report. We identify additional sufficient conditions on the joint distribution for a posted price to be an optimal mechanism. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio types are independently distributed. |
| Keywords: | optimal mechanism, complementary goods, multidimensional private information, posted-price mechanism |
| JEL: | D82 D40 D42 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:alo:isipdp:21-01&r=all |
| By: | Santiago Balseiro; Christian Kroer; Rachitesh Kumar |
| Abstract: | The internet advertising market is a multi-billion dollar industry, in which advertisers buy thousands of ad placements every day by repeatedly participating in auctions. In recent years, the industry has shifted to first-price auctions as the preferred paradigm for selling advertising slots. Another important and ubiquitous feature of these auctions is the presence of campaign budgets, which specify the maximum amount the advertisers are willing to pay over a specified time period. In this paper, we present a new model to study the equilibrium bidding strategies in first-price auctions for advertisers who satisfy budget constraints on average. Our model dispenses with the common, yet unrealistic assumption that advertisers' values are independent and instead assumes a contextual model in which advertisers determine their values using a common feature vector. We show the existence of a natural value-pacing-based Bayes-Nash equilibrium under very mild assumptions, and study its structural properties. Furthermore, we generalize the existence result to standard auctions and prove a revenue equivalence showing that all standard auctions yield the same revenue even in the presence of budget constraints. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.10476&r=all |
| By: | Dengji Zhao |
| Abstract: | Mechanism design has traditionally assumed that the set of participants are fixed and known to the mechanism (the market owner) in advance. However, in practice, the market owner can only directly reach a small number of participants (her neighbours). Hence the owner often needs costly promotions to recruit more participants in order to get desirable outcomes such as social welfare or revenue maximization. In this paper, we propose to incentivize existing participants to invite their neighbours to attract more participants. However, they would not invite each other if they are competitors. We discuss how to utilize the conflict of interest between the participants to incentivize them to invite each other to form larger markets. We will highlight the early solutions and open the floor for discussing the fundamental open questions in the settings of auctions, coalitional games, matching and voting. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.10347&r=all |
| By: | Geoffroy de Clippel; Rene Saran; Roberto Serrano |
| Abstract: | In de Clippel, Saran, and Serrano (2019), it is shown that, perhaps surprisingly, the set of implementable social choice functions is essentially the same whether agents have bounded depth of reasoning or rational expectations. The picture is quite different when taking into account the possibility of small modeling mistakes. While continuous strict implementation becomes very demanding (Oury and Tercieux (2012) Ð OT), continuity in level-k implementation obtains essentially for free. A decomposition of the conditions implied by the OT implementation notion confirms that it is the use of equilibrium, and not continuity per se, that is responsible for the difference. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2021-002&r=all |
| By: | Andrew Jennings; Rida Laraki; Clemens Puppe; Estelle Varloot |
| Abstract: | We provide novel simple representations of strategy-proof voting rules when voters have uni-dimensional single-peaked preferences (as well as multi-dimensional separable preferences). The analysis recovers, links and unifies existing results in the literature such as Moulin's classic characterization in terms of phantom voters and Barber\`a, Gul and Stacchetti's in terms of winning coalitions ("generalized median voter schemes"). First, we compare the computational properties of the various representations and show that the grading curve representation is superior in terms of computational complexity. Moreover, the new approach allows us to obtain new characterizations when strategy-proofness is combined with other desirable properties such as anonymity, responsiveness, ordinality, participation, consistency, or proportionality. In the anonymous case, two methods are single out: the -- well know -- ordinal median and the -- most recent -- linear median. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.11686&r=all |
| By: | Michela Chessa (Université Côte d'Azur, France; GREDEG CNRS); Nobuyuki Hanaki (Osaka University,); Aymeric Lardon (GATE Lyon Saint-Etienne,); Takashi Yamada (Yamaguchi University, Japan) |
| Abstract: | We experimentally compare two well-known mechanisms inducing the Shapley value as an ex ante equilibrium outcome of a noncooperative bargaining procedure: the demand-based Winter's demand commitment bargaining mechanism and the offer-based Hart and Mas-Colell bidding procedure. Our results suggest that, on the one hand, the offer-based Hart and Mas-Colell mechanism better induces players to cooperate and to agree on an efficient outcome; on the other hand, the demand-based Winter mechanism better implements allocations that reflect players' effective bargaining power. |
| Keywords: | Nash Program, Bargaining procedures, Shapley value, Experiments |
| JEL: | C71 C72 C90 D82 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2021-07&r=all |