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on Economic Design |
| By: | Richard P. McLean (Rutgers University); Andrew Postlewaite (University of Pennsylvania) |
| Abstract: | Standard mechanism design begins with a statement of the problem, including knowledge on the designer's part about the distribution of the characteristics (preferences and information) of the participants who are to engage with the mechanism. There is a large literature on robust mechanism design, much of which aims to reduce the assumed information the designer has about the participants. In this paper we provide an auction mechanism that reduces the assumed information assumed of the seller, and, in addition, relaxes substantially the assumed information of the participants. In particular, the mechanism performs well when there are many buyers, even though there is no prior distribution over the accuracy of buyers' information on the part of the designer or the participants. |
| Keywords: | Robustness, Optimal auctions, Incentive Compatibility, Mechanism Design, Interdependent Values, Informational Size, Common Knowledge |
| JEL: | C70 D44 D60 D82 |
| Date: | 2024–10–31 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:24-035 |
| By: | Pablo Neme; Jorge Oviedo |
| Abstract: | For a many-to-one market with substitutable preferences on the firm's side, based on the Aizerman-Malishevski decomposition, we define an associated one-to-one market. Given that the usual notion of stability for a one-to-one market does not fit well for this associated one-to-one market, we introduce a new notion of stability. This notion allows us to establish an isomorphism between the set of stable matchings in the many-to-one market and the matchings in the associated one-to-one market that meet this new stability criterion. Furthermore, we present an adaptation of the well-known deferred acceptance algorithm to compute a matching that satisfies this new notion of stability for the associated one-to-one market. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.00564 |
| By: | Li, Jiangtao (Singapore Management University); Wang, Kexin (Singapore Management University) |
| Abstract: | We study the design of mechanisms when the mechanism designer faces local uncertainty about agents’ beliefs. Specifically, we consider a designer who does not know the exact beliefs of the agents but is confident that her estimate is within of the beliefs held by the agents (where reflects the degree of local uncertainty). Adopting the robust optimization approach, we design mechanisms that incentivize agents to truthfully report their payoff-relevant information regardless of their actual beliefs. For any fixed, we identify necessary and sufficient conditions under which requiring this sense of robustness is without loss of revenue for the designer. By analyzing the limiting case in which approaches 0, we provide two rationales for the widely studied Bayesian mechanism design framework. |
| Date: | 2024–08–12 |
| URL: | https://d.repec.org/n?u=RePEc:ris:smuesw:2024_008 |
| By: | Jeon, Doh-Shin; Ichihashi, Shota; Kim, Byung-Cheol |
| Abstract: | We study a mechanism design problem of a monopoly platform that matches content of varying quality, ads with dierent ad revenues, and consumers with heterogeneous tastes for content quality. The optimal mechanism balances revenue from advertising and revenue from selling access to content: Increasing advertising revenue requires serving content to more consumers, which may reduce access revenue. Contrary to the standard monopolistic screening, the platform may serve content to consumers with negative virtual values while, to reduce information rents, limiting their access to higher-quality content. Then, an increase in ad protability reduces its incentive to invest in content quality. |
| JEL: | D42 D82 L15 O31 |
| Date: | 2024–11–13 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129923 |
| By: | Ilya Hajiaghayi; MohammadTaghi Hajiaghayi; Gary Peng; Suho Shin |
| Abstract: | We study bilateral trade with a broker, where a buyer and seller interact exclusively through the broker. The broker strategically maximizes her payoff through arbitrage by trading with the buyer and seller at different prices. We study whether the presence of the broker interferes with the mechanism's gains-from-trade (GFT) achieving a constant-factor approximation to the first-best gains-from-trade (FB). We first show that the GFT achieves a $1 / 36$-approximation to the FB even if the broker runs an optimal posted-pricing mechanism under symmetric agents with monotone-hazard-rate distributions. Beyond posted-pricing mechanisms, even if the broker uses an arbitrary incentive-compatible (IC) and individually-rational (IR) mechanism that maximizes her expected profit, we prove that it induces a $1 / 2$-approximation to the first-best GFT when the buyer and seller's distributions are uniform distributions with arbitrary support. This bound is shown to be tight. We complement such results by proving that if the broker uses an arbitrary profit-maximizing IC and IR mechanism, there exists a family of problem instances under which the approximation factor to the first-best GFT becomes arbitrarily bad. We show that this phenomenon persists even if we restrict one of the buyer's or seller's distributions to have a singleton support, or even in the symmetric setting where the buyer and seller have identical distributions. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17444 |
| By: | Mohit Garg; N. Raja; Suneel Sarswat; Abhishek Kr Singh |
| Abstract: | Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how these requests are to be matched. The two most common objectives for determining the matching are maximizing trade volume at a uniform price and maximizing trade volume through dynamic pricing. Prior research has primarily focused on single-quantity trade requests. In this work, we extend the framework to handle multiple-quantity trade requests and present fully formalized matching algorithms for double auctions, along with their correctness proofs. We establish new uniqueness theorems, enabling automatic detection of violations in exchange systems by comparing their output to that of a verified program. All proofs are formalized in the Coq Proof Assistant, and we extract verified OCaml and Haskell programs that could serve as a resource for exchanges and market regulators. We demonstrate the practical applicability of our work by running the verified program on real market data from an exchange to automatically check for violations in the exchange algorithm. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18751 |
| By: | Emir Kamenica; Xiao Lin |
| Abstract: | When does a Sender, in a Sender-Receiver game, strictly value commitment? In a setting with finite actions and finite states, we establish that, generically, Sender values commitment if and only if he values randomization. In other words, commitment has no value if and only if a partitional experiment is optimal under commitment. Moreover, if Sender's preferred cheap-talk equilibrium necessarily involves randomization, then Sender values commitment. We also ask: how often (i.e., for what share of preference profiles) does commitment have no value? For any prior, any independent, atomless distribution of preferences, and any state space: if there are $\left|A\right|$ actions, the likelihood that commitment has no value is at least $\frac{1}{\left|A\right|^{\left|A\right|}}$. As the number of states grows large, this likelihood converges precisely to $\frac{1}{\left|A\right|^{\left|A\right| }}$. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17503 |
| By: | Flores-Szwagrzak, Karol (Department of Economics, Copenhagen Business School); Østerdal, Lars Peter (Department of Economics, Copenhagen Business School) |
| Abstract: | A partnership can yield a return—a loss or a profit relative to the partners’ investments. How should the partners share the return? We identify the shar-ing rules satisfying classical properties (symmetry, consistency, and continuity) and avoiding arbitrary bounds on a partner’s share. We show that any such rule can be rationalized in the sense that its recommendations are aligned with those maximizing a separable welfare function. Among these rules, we charac-terize those formalizing different notions of proportionality and, in particular, a convenient subclass specified by a single inequality aversion parameter. We also explore when a rule can be rationalized by a more general welfare function. Our central results extend to a wider class of resource allocation problems. |
| Keywords: | Sharing; Consistency; Axioms; Welfare maximization |
| JEL: | D63 D70 D71 |
| Date: | 2024–11–11 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:cbsnow:2024_017 |
| By: | Javier Cembrano; Jos\'e Correa; Ulrike Schmidt-Kraepelin; Alexandros Tsigonias-Dimitriadis; Victor Verdugo |
| Abstract: | The apportionment problem constitutes a fundamental problem in democratic societies: How to distribute a fixed number of seats among a set of states in proportion to the states' populations? This--seemingly simple--task has led to a rich literature and has become well known in the context of the US House of Representatives. In this paper, we connect the design of monotone apportionment methods to classic problems from discrete geometry and combinatorial optimization and explore the extent to which randomization can enhance proportionality. We first focus on the well-studied family of stationary divisor methods, which satisfy the strong population monotonicity property, and show that this family produces only a slightly superlinear number of different outputs as a function of the number of states. While our upper and lower bounds leave a small gap, we show that--surprisingly--closing this gap would solve a long-standing open problem from discrete geometry, known as the complexity of $k$-levels in line arrangements. The main downside of divisor methods is their violation of the quota axiom, i.e., every state should receive $\lfloor q_i\rfloor$ or $\lceil q_i\rceil$ seats, where $q_i$ is the proportional share of the state. As we show that randomizing over divisor methods can only partially overcome this issue, we propose a relaxed version of divisor methods in which the total number of seats may slightly deviate from the house size. By randomizing over them, we can simultaneously satisfy population monotonicity, quota, and ex-ante proportionality. Finally, we turn our attention to quota-compliant methods that are house-monotone, i.e., no state may lose a seat when the house size is increased. We provide a polyhedral characterization based on network flows, which implies a simple description of all ex-ante proportional randomized methods that are house-monotone and quota-compliant. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.23869 |
| By: | Ziv Scully; Laura Doval |
| Abstract: | We consider search problems with nonobligatory inspection and single-item or combinatorial selection. A decision maker is presented with a number of items, each of which contains an unknown price, and can pay an inspection cost to observe the item's price before selecting it. Under single-item selection, the decision maker must select one item; under combinatorial selection, the decision maker must select a set of items that satisfies certain constraints. In our nonobligatory inspection setting, the decision maker can select items without first inspecting them. It is well-known that search with nonobligatory inspection is harder than the well-studied obligatory inspection case, for which the optimal policy for single-item selection (Weitzman, 1979) and approximation algorithms for combinatorial selection (Singla, 2018) are known. We introduce a technique, local hedging, for constructing policies with good approximation ratios in the nonobligatory inspection setting. Local hedging transforms policies for the obligatory inspection setting into policies for the nonobligatory inspection setting, at the cost of an extra factor in the approximation ratio. The factor is instance-dependent but is at most 4/3. We thus obtain the first approximation algorithms for a variety of combinatorial selection problems, including matroid basis, matching, and facility location. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.19011 |
| By: | Martimort, David; Stole, Lars |
| Abstract: | We study menu auction games in which several principals influence the choice of a privately-informed agent by simultaneously offering action-contingent payments; the agent is free to accept any subset of the offers. Building on tools from non-smooth optimal control with type-dependent participation constraints, we provide necessary conditions for any equilibrium allocation as the (constrained) maximizer of an endogenous aggregate virtual-surplus program. The aggregate maximand includes an information-rent component which captures how the principals’ rent-extraction motives combine. Although there is a large set of equilibria, including equilibrium allocations with discontinuities, we isolate one particular equilibrium allocation, the maximal allocation, which is the solution to an unconstrained maximization program. Under weak conditions, necessary conditions for a maximal allocation are also sufficient, and the corresponding equilibrium tariff offers are easily constructed. We illustrate our findings and derive some economic implications in several applications, with principals having either congruent interests (e.g., public goods collective action games), opposed interests (e.g., pork barrel politics, lobbying), and protection for sale in an international trade context. |
| Keywords: | Menu auctions;; delegated common agency;; screening contracts;; non-smooth optimization problems;; public goods games; ; collective action;; pork barrel politics; ; positive theory of regulation;; protection for sale |
| Date: | 2024–11–14 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129924 |