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on Economic Design |
| By: | Elliott, M.; Galeotti, A.; Koh, A.; Li, W. |
| Abstract: | There are many markets that are networked in these sense that not all consumers have access to (or are aware of) all products, while, at the same time, firms have some information about consumers and can distinguish some consumers from some others (for example, in online markets through cookies). With unit demand and price-setting firms we give a complete characterization of all welfare outcomes achievable in equilibrium (for arbitrary buyer-seller networks and arbitrary information structures), as well as the designs (networks and information structures) which implement them. |
| Date: | 2023–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camjip:2304&r=des |
| By: | Kirill Rudov |
| Abstract: | We show how fragile stable matchings are in a decentralized one-to-one matching setting. The classical work of Roth and Vande Vate (1990) suggests simple decentralized dynamics in which randomly-chosen blocking pairs match successively. Such decentralized interactions guarantee convergence to a stable matching. Our first theorem shows that, under mild conditions, any unstable matching -- including a small perturbation of a stable matching -- can culminate in any stable matching through these dynamics. Our second theorem highlights another aspect of fragility: stabilization may take a long time. Even in markets with a unique stable matching, where the dynamics always converge to the same matching, decentralized interactions can require an exponentially long duration to converge. A small perturbation of a stable matching may lead the market away from stability and involve a sizable proportion of mismatched participants for extended periods. Our results hold for a broad class of dynamics. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.12183&r=des |
| By: | Daniela Bubboloni; Michele Gori; Claudia Meo |
| Abstract: | We focus on the basic one-to-one two-sided matching model, where there are two disjoint sets of agents of equal size, and each agent in a set has preferences on the agents in the other set, modelled by linear orders. The goal is to find a matching that associates each agent in one set with one and only one agent in the other set based on the agents' preferences. A mechanism is a rule that associates a set of matchings to each preference profile. Stability, which refers to the capability to select only stable matchings, is an important property a mechanism should fulfill. Another crucial property, especially useful for applications, is resoluteness, which requires that the mechanism always selects a unique matching. The two versions of the deferred acceptance algorithm are examples of stable and resolute mechanisms. However, these mechanisms are severely unfair since they strongly favor one of the two sides of the market. In this paper, we introduce a property that mechanisms may meet which relates to fairness. Such property, called symmetry, is formulated in a way able to capture different levels of fairness within and across the two sets of agents and generalize existing notions. We prove several possibility and impossibility results, mainly involving the most general notion of symmetry, known as gender fairness: among others, a resolute and gender fair mechanism exists if and only if each side of the market consists of an odd number of agents; there exists no resolute, stable and gender fair mechanism. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.01404&r=des |
| By: | Pham, Hien |
| Abstract: | A monopolistic seller jointly designs allocation rules and (new) information about a pay-off relevant state to a buyer with private types. When the new information flips the ranking of willingness to pay across types, a screening menu of prices and threshold disclosures is optimal. Conversely, when its impact is marginal, bunching via a single posted price and threshold disclosure is (approximately) optimal. While information design expands the scope for random mechanisms to outperform their deterministic counterparts, its presence leads to an equivalence result regarding sequential versus. static screening. |
| Keywords: | mechanism design, information design, sequential screening, random mechanisms, bunching. |
| JEL: | D42 D82 D86 L15 |
| Date: | 2023–04–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120462&r=des |
| By: | Peyman Khezr; Vijay Mohan; Lionel Page |
| Abstract: | In the Knapsack Problem a set of indivisible objects, each with different values and sizes, must be packed into a fixed-size knapsack to maximize the total value. The knapsack problem is known to be an NP-hard problem even when there is full information regarding values and sizes. In many real-world situations, however, the values of objects are private information, which adds another dimension of complexity. In this paper we examine the knapsack problem with private information by investigating three practical auctions as possible candidates for payment rules in a setup where the knapsack owner sells the space to object owners via an auction. The three auctions are the discriminatory price, the generalized second-price and the uniform-price auctions. Using a Greedy algorithm for allocating objects, we analyze bidding behavior, revenue and efficiency of these three auctions using theory, lab experiments, and AI-enriched simulations. Our results suggest that the uniform-price auction has the highest level of truthful bidding and efficiency while the discriminatory price and the generalized second-price auctions are superior in terms of revenue generation. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.07928&r=des |
| By: | Clayton Thomas |
| Abstract: | Stable matchings are a cornerstone of market design, with numerous practical deployments backed by a rich, theoretically-tractable structure. However, in school-choice problems, stable matchings are not Pareto optimal for the students. Priority-neutral matchings, introduced by Reny (AER, 2022), generalizes the set of stable matchings by allowing for certain priority violations, and there is always a Pareto optimal priority-neutral matching. Moreover, like stable matchings, the set of priority-neutral matchings forms a lattice. We study the structure of the priority-neutral lattice. Unfortunately, we show that much of the simplicity of the stable matching lattice does not hold for the priority-neutral lattice. In particular, we show that the priority-neutral lattice need not be distributive. Moreover, we show that the greatest lower bound of two matchings in the priority-neutral lattice need not be their student-by-student minimum, answering an open question. This show that many widely-used properties of stable matchings fail for priority-neutral matchings; in particular, the set of priority-neutral matchings cannot be represented by via a partial ordering on a set of rotations. However, by proving a novel structural property of the set of priority-neutral matchings, we also show that not every lattice arises as a priority-neutral lattice, which suggests that the exact nature of the family of priority-neutral lattices may be subtle. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.02142&r=des |
| By: | Luca Anderlini; GaOn Kim |
| Abstract: | We examine ``tournament'' second-price auctions in which $N$ bidders compete for the right to participate in a second stage and contend against bidder $N+1$. When the first $N$ bidders are committed so that their bids cannot be changed in the second stage, the analysis yields some unexpected results. The first $N$ bidders consistently bid above their values in equilibrium. When bidder $N+1$ is sufficiently stronger than the first $N$, overbidding leads to an increase in expected revenue in comparison to the standard second-price auction when $N$ is large. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.08102&r=des |
| By: | Ian Ball; Teemu Pekkarinen |
| Abstract: | We study the design of an auction for a license. Each agent has a signal about his future profit from winning the license. If the license is allocated, the winner can be charged a flexible royalty based on the profits he reports. The principal can audit the winner, at a cost, and charge limited penalties. We solve for the auction that maximizes revenue, net auditing costs. In this auction, the winner pays linear royalties up to a cap, beyond which there is no auditing. A more optimistic bidder pays more upfront in exchange for a lower royalty cap. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.19945&r=des |
| By: | Triêu, Anh (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory); Bos, Iwan (RS: GSBE other - not theme-related research, Organisation, Strategy & Entrepreneurship); Schröder, Marc (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory); Vermeulen, Dries (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory, RS: FSE DACS Mathematics Centre Maastricht) |
| Abstract: | There are many situations in which policymakers are primarily concerned with the availability and accessibility of goods or services. Examples include electricity, food, housing, medical supplies, et cetera. In such cases, the social goal may be to maximize the number of transactions, which we refer to as a maximal matching. This paper presents a mechanism that implements this objective. The mechanism satisfies the incentive and participation constraints, but requires external funding. |
| JEL: | C72 D47 D63 |
| Date: | 2024–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2024004&r=des |