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on Economic Design |
| By: | Ian Ball; Deniz Kattwinkel |
| Abstract: | The maxmin approach to distributional robustness evaluates each mechanism according to its payoff guarantee over all priors in an ambiguity set. We propose a refinement: the guarantee must be approximately satisfied at priors near the ambiguity set (in the weak topology). We call such a guarantee robust. The payoff guarantees from some maxmin-optimal mechanisms in the literature are not robust. We show, however, that over certain standard ambiguity sets (such as continuous moment sets), every mechanism's payoff guarantee is robust. We give a behavioral characterization of our refined robustness notion by imposing a new continuity axiom on maxmin preferences. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.16898 |
| By: | Shixin Wang |
| Abstract: | It is generally challenging to characterize the optimal selling mechanism even when the seller knows the buyer's valuation distributions in multi-item screening. An insightful and significant result in robust mechanism design literature is that if the seller knows only marginal distributions of the buyer's valuation, then separable mechanisms, in which all items are sold independently, are robustly optimal under the maximin revenue objectives. While the separable mechanism is simple to implement, the literature also indicates that separate selling can not guarantee any substantial fraction of the potential optimal revenue for given distributions. To design a simple mechanism with a good performance guarantee, we introduce a novel class of mechanisms, termed "semi-separable mechanism". In these mechanisms, the allocation and payment rule of each item is a function solely of the corresponding item's valuation, which retains the separable mechanism's practical simplicity. However, the design of the allocation and payment function is enhanced by leveraging the joint distributional information, thereby improving the performance guarantee against the hindsight optimal revenue. We establish that a semi-separable mechanism achieves the optimal performance ratio among all incentive-compatible and individually rational mechanisms when only marginal support information is known. This result demonstrates that the semi-separable mechanisms ensure both the interpretation and implementation simplicity, and performance superiority. Our framework is also applicable to scenarios where the seller possesses information about the aggregate valuations of product bundles within any given partition of the product set. Furthermore, our results also provide guidelines for the multi-item screening problem with non-standard ambiguity sets. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.13580 |
| By: | Wei He; Jiangtao Li; Weijie Zhong |
| Abstract: | We propose a combinatorial ascending auction that is "approximately" optimal, requiring minimal rationality to achieve this level of optimality, and is robust to strategic and distributional uncertainties. Specifically, the auction is rank-guaranteed, meaning that for any menu M and any valuation profile, the ex-post revenue is guaranteed to be at least as high as the highest revenue achievable from feasible allocations, taking the (|M|+ 1)th-highest valuation for each bundle as the price. Our analysis highlights a crucial aspect of combinatorial auction design, namely, the design of menus. We provide simple and approximately optimal menus in various settings. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.12001 |
| By: | Zhen Zhao |
| Abstract: | We study the problem of allocating a single indivisible good to at most one of n agents when the preferences of agents' are quasilinear, monetary transfers are allowed and strategy-proof mechanism is needed. In this paper, we consider the possibility of constructing feasible allocation mechanisms which satisfy strategy-proofness, anonymity, budget balance and no wastage. In two and three agents cases, we show an impossibility result. |
| Date: | 2024–09–05 |
| URL: | https://d.repec.org/n?u=RePEc:toh:tupdaa:52 |
| By: | Shunya Noda; Genta Okada |
| Abstract: | We study efficient mechanism design for allocating multiple heterogeneous objects. We aim to maximize the residual surplus, the total value generated from an allocation minus the costs for screening agents' values. We discover a robust trend indicating that no-screening mechanisms such as serial dictatorship with exogenous priority order tend to perform better as the variety of goods increases. We analyze the underlying reasons by characterizing efficient mechanisms in a stylized environment. We also apply an automated mechanism design approach to numerically derive efficient mechanisms and validate the trend in general environments. Building on this implication, we propose the register-invite-book system (RIB) as an efficient system for scheduling vaccination against pandemic diseases. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.10077 |
| By: | Leonardo Matone; Ben Abramowitz; Nicholas Mattei; Avinash Balakrishnan |
| Abstract: | Aggregating the preferences of multiple agents into a collective decision is a common step in many important problems across areas of computer science including information retrieval, reinforcement learning, and recommender systems. As Social Choice Theory has shown, the problem of designing algorithms for aggregation rules with specific properties (axioms) can be difficult, or provably impossible in some cases. Instead of designing algorithms by hand, one can learn aggregation rules, particularly voting rules, from data. However, the prior work in this area has required extremely large models, or been limited by the choice of preference representation, i.e., embedding. We recast the problem of designing a good voting rule into one of learning probabilistic versions of voting rules that output distributions over a set of candidates. Specifically, we use neural networks to learn probabilistic social choice functions from the literature. We show that embeddings of preference profiles derived from the social choice literature allows us to learn existing voting rules more efficiently and scale to larger populations of voters more easily than other work if the embedding is tailored to the learning objective. Moreover, we show that rules learned using embeddings can be tweaked to create novel voting rules with improved axiomatic properties. Namely, we show that existing voting rules require only minor modification to combat a probabilistic version of the No Show Paradox. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.13630 |
| By: | Debasis Mishra; Sanket Patil |
| Abstract: | We study undominated mechanisms with transfers for regulating a monopolist who privately observes the marginal cost of production. We show that in any undominated mechanism, there is a quantity floor, which depends only on the primitives, and the regulator's operation decision is stochastic only if the monopolist produces at the quantity floor. We provide a near-complete characterization of the set of undominated mechanisms and use it to (a) provide a foundation for deterministic mechanisms, (b) show that the efficient mechanism is dominated, and (c) derive a max-min optimal regulatory mechanism. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.09473 |
| By: | Michael Finus (University of Graz, Austria) |
| Abstract: | Kornek and Edenhofer (2020) propose a transfer scheme in the spirit of mechanism design in a two-stage coalition formation game. Not only non-signatories but also signatories choose their provision levels non-cooperatively. They show that the grand coalition is stable, implementing the socially optimal provision level. McEvoy and McGinty (2023) argue in a comment that this scheme is flawed as it does not address free-riding in the sense of non-compliance. I offer a solution to the problem highlighted by McEvoy and McGinty (2023), proposing a modification of the original set-up which addresses both dimensions of free-riding. I demonstrate that the scheme also works for asymmetric countries. |
| Keywords: | Global Public Goods, Agreements, Membership, Compliance. |
| JEL: | C71 C72 D70 H41 Q54 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2024-14 |
| By: | Jean-Michel Benkert; Armin Schmutzler |
| Abstract: | This paper investigates the value of recommendations for disseminating economic information, with a focus on frictions resulting from preference heterogeneity. We consider Bayesian expected-payoff maximizers who receive non-strategic recommendations by other consumers. The paper provides conditions under which different consumer types accept these recommendations. Moreover, we assess the overall value of a recommendation system and the determinants of that value. Our analysis highlights the importance of disentangling objective information from subjective preferences when designing value-maximizing recommendation systems. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.11362 |
| By: | Kiho Yoon |
| Abstract: | We study the equilibria of uniform price auctions where bidders have flat demands up to their respective quantity constraints. We present an iterative procedure that systematically finds a Nash equilibrium outcome under semi-complete information as well as a novel ascending auction under incomplete information that has this outcome as a dominant strategy equilibrium. Demand reduction and low price equilibrium may occur since it is sometimes advantageous for a bidder to give up some of his/her demand and get the remaining demand at a low price rather than to get his/her entire demand at a higher price. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.04047 |
| By: | Subiza, Begoña (Universitat d’Alacant, MQiTE and IUDESP.); Jiménez-Gómez, José Manuel (Universitat Rovira i Virgili, Dept. d’Economia and ECO-SOS); Peris, Josep E (Universitat d’Alacant, MQiTE and IUDESP.) |
| Abstract: | A minimum cost spanning tree problem analyzes the way to efficiently connect agents to a source when they are located at different places. Estévez-Fernández and Reijnierse (2014) study minimum cost spanning tree problems with revenues (agents can obtain a benefit, if they are connected to the source) and show that the cost-revenues game may have an empty core. In this context, we provide a non-empty unique set that coincides with the core, whenever the core is not empty. In so doing, we define a dominance relation among individually rational distributions of the net revenue and compute the von Neumann-Morgenstern stable set regarding this dominance relation. It is important to highlight that the dominance relation is based on the fact that a majority of agents do not block the sharing of the net revenue. |
| Keywords: | Minimum cost spanning tree; Cost-revenues game; Core; Stable set |
| JEL: | C71 D63 D71 |
| Date: | 2024–09–03 |
| URL: | https://d.repec.org/n?u=RePEc:ris:qmetal:2024_005 |
| By: | Albrecht, James (Georgetown University); Cai, Xiaoming (Peking University); Gautier, Pieter A. (Vrije Universiteit Amsterdam); Vroman, Susan (Georgetown University) |
| Abstract: | This paper considers competitive search equilibrium in a market for a good whose quality differs across sellers. Each seller knows the quality of the good that he or she is offering for sale, but buyers cannot observe quality directly. We thus have a "market for lemons" with competitive search frictions. In contrast to Akerlof (1970), we prove the existence of a unique equilibrium, which is separating. Higher-quality sellers post higher prices, so price signals quality. The arrival rate of buyers is lower in submarkets with higher prices, but this is less costly for higher-quality sellers given their higher continuation values. For some parameter values, higher-quality sellers post the full-information price; for other values these sellers have to post a higher price to keep lower-quality sellers from mimicking them. In an extension, we show that if sellers compete with auctions, the reserve price can also act as a signal. |
| Keywords: | competitive search, signaling |
| JEL: | C78 D82 D83 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17246 |
| By: | Andrew Koh; Sivakorn Sanguanmoo |
| Abstract: | We analyze how uncertain technologies should be robustly regulated. An agent develops a new technology and, while privately learning about its harms and benefits, continually chooses whether to continue development. A principal, uncertain about what the agent might learn, chooses among dynamic mechanisms (e.g., paths of taxes or subsidies) to influence the agent's choices in different states. We show that learning robust mechanisms -- those which deliver the highest payoff guarantee across all learning processes -- are simple and resemble `regulatory sandboxes' consisting of zero marginal tax on R&D which keeps the agent maximally sensitive to new information up to a hard quota, upon which the agent turns maximally insensitive. Robustness is important: we characterize the worst-case learning process under non-robust mechanisms and show that they induce growing but weak optimism which can deliver unboundedly poor principal payoffs; hard quotas safeguard against this. If the regulator also learns, adaptive hard quotas are robustly optimal which highlights the importance of expertise in regulation. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.17398 |