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on Economic Design |
| By: | Vikram Manjunath; Alexander Westkamp |
| Abstract: | We consider the balanced exchange of bundles of indivisible goods. We are interested in mechanisms that only rely on marginal preferences over individual objects even though agents' actual preferences compare bundles. Such mechanisms play an important role in two-sided matching but have not received much attention in exchange settings. We show that individually rational and Pareto-efficient marginal mechanisms exist if and only if no agent ever ranks any of her endowed objects lower than in her second indifference class. We call such marginal preferences trichotomous. In proving sufficiency, we define mechanisms, which are constrained versions of serial dictatorship, that achieve both desiderata based only agents' marginal preferences. We then turn to strategy-proofness. An individually rational, efficient and strategy-proof mechanism-marginal or not-exists if and only if each agent's marginal preference is not only trichotomous, but does not contain a non-endowed object in her second indifference class. We call such marginal preferences strongly trichotomous. For such preferences, our mechanisms reduce to the class of strategy-proof mechanisms introduced in Manjunath and Westkamp (2018). For trichotomous preferences, while our variants of serial dictatorship are not strategy-proof, they are truncation-proof and not obviously manipulable (Troyan and Morrill, 2020). |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.06499 |
| By: | Ruiqin Wang; Cagil Kocyigit; Napat Rujeerapaiboon |
| Abstract: | We study a mechanism design problem where a seller aims to allocate a good to multiple bidders, each with a private value. The seller supports or favors a specific group, referred to as the minority group. Specifically, the seller requires that allocations to the minority group are at least a predetermined fraction (equity level) of those made to the rest of the bidders. Such constraints arise in various settings, including government procurement and corporate supply chain policies that prioritize small businesses, environmentally responsible suppliers, or enterprises owned by historically disadvantaged individuals. We analyze two variants of this problem: stochastic mechanism design, which assumes bidders' values follow a known distribution and seeks to maximize expected revenue, and regret-based mechanism design, which makes no distributional assumptions and aims to minimize the worst-case regret. We characterize a closed-form optimal stochastic mechanism and propose a closed-form regret-based mechanism, and establish that the ex-post regret under the latter is at most a constant multiple (dependent on the equity level) of the optimal worst-case regret. We further quantify that this approximation constant is at most 1.31 across different equity levels. Both mechanisms can be interpreted as set-asides, a common policy tool that reserves a fraction of goods for minority groups. Furthermore, numerical results demonstrate that the stochastic mechanism performs well when the bidders' value distribution is accurately estimated, while the regret-based mechanism exhibits greater robustness under estimation errors. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.08369 |
| By: | Aram Grigoryan; Markus Möller |
| Keywords: | Allocation Problems, Robust Market Design, Opaque Announcements, Strategy-Proofness, Transparency We introduce a framework where the announcements of a clearinghouse about the allocation process are opaque in the sense that there can be more than one outcome compatible with a realization of type reports. We ask whether desirable properties can be ensured under opacity in a robust sense. A property can be guaranteed under an opaque announcement if every mechanism compatible with it satisfies the property. We find an impossibility result: strategy-proofness cannot be guaranteed under any level of opacity. In contrast, in some environments, weak Maskin monotonicity and non-bossiness can be guaranteed under opacity. |
| JEL: | C78 D47 D82 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_653 |
| By: | Eden Hartman; Erel Segal-Halevi; Biaoshuai Tao |
| Abstract: | The classic notion of truthfulness requires that no agent has a profitable manipulation -- an untruthful report that, for some combination of reports of the other agents, increases her utility. This strong notion implicitly assumes that the manipulating agent either knows what all other agents are going to report, or is willing to take the risk and act as-if she knows their reports. Without knowledge of the others' reports, most manipulations are risky -- they might decrease the manipulator's utility for some other combinations of reports by the other agents. Accordingly, a recent paper (Bu, Song and Tao, ``On the existence of truthful fair cake cutting mechanisms'', Artificial Intelligence 319 (2023), 103904) suggests a relaxed notion, which we refer to as risk-avoiding truthfulness (RAT), which requires only that no agent can gain from a safe manipulation -- one that is sometimes beneficial and never harmful. Truthfulness and RAT are two extremes: the former considers manipulators with complete knowledge of others, whereas the latter considers manipulators with no knowledge at all. In reality, agents often know about some -- but not all -- of the other agents. This paper introduces the RAT-degree of a mechanism, defined as the smallest number of agents whose reports, if known, may allow another agent to safely manipulate, or $n$ if there is no such number. This notion interpolates between classic truthfulness (degree $n$) and RAT (degree at least $1$): a mechanism with a higher RAT-degree is harder to manipulate safely. To illustrate the generality and applicability of this concept, we analyze the RAT-degree of prominent mechanisms across various social choice settings, including auctions, indivisible goods allocations, cake-cutting, voting, and stable matchings. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.18805 |
| By: | Dirk Bergemann; Rahul Deb |
| Abstract: | We study the robust sequential screening problem of a monopolist seller of multiple cloud computing services facing a buyer who has private information about his demand distribution for these services. At the time of contracting, the buyer knows the distribution of his demand of various services and the seller simply knows the mean of the buyer's total demand. We show that a simple "committed spend mechanism" is robustly optimal: it provides the seller with the highest profit guarantee against all demand distributions that have the known total mean demand. This mechanism requires the buyer to commit to a minimum total usage and a corresponding base payment; the buyer can choose the individual quantities of each service and is free to consume additional units (over the committed total usage) at a fixed marginal price. This result provides theoretical support for prevalent cloud computing pricing practices while highlighting the robustness of simple pricing schemes in environments with complex uncertainty. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.07168 |
| By: | Aram Grigoryan; Markus Möller |
| Keywords: | Matching and Allocation, Auditability, Deviation Detection, In centralized mechanisms and platforms, participants do not fully observe each others' type reports. Hence, if there is a deviation from the promised mechanism, participants may be unable to detect it. We formalize a notion of auditabilty that captures how easy or hard it is to detect deviations from a mechanism. We find a stark contrast between the auditabilities of prominent mechanisms. We also provide tight characterizations of maximally auditable classes of allocation mechanisms. |
| JEL: | C78 D47 D82 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_652 |
| By: | Shengyuan Huang; Wenjun Mei; Xiaoguang Yang; Zhigang Cao |
| Abstract: | This paper studies allocation mechanisms in max-flow games with players' capacities as private information. We first show that no core-selection mechanism is truthful: there may exist a player whose payoff increases if she under-reports her capacity when a core-section mechanism is adopted. We then introduce five desirable properties for mechanisms in max-flow games: DSIC (truthful reporting is a dominant strategy), SIR (individual rationality and positive payoff for each player contributing positively to at least one coalition), SP (no edge has an incentive to split into parallel edges), MP (no parallel edges have incentives to merge), and CM (a player's payoff does not decrease as another player's capacity and max-flow increase). While the Shapley value mechanism satisfies DSIC and SIR, it fails to meet SP, MP and CM. We propose a new mechanism based on minimal cuts that satisfies all five properties. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.08248 |
| By: | Yan Dai; Moise Blanchard; Patrick Jaillet |
| Abstract: | We study a repeated resource allocation problem with strategic agents where monetary transfers are disallowed and the central planner has no prior information on agents' utility distributions. In light of Arrow's impossibility theorem, acquiring information about agent preferences through some form of feedback is necessary. We assume that the central planner can request powerful but expensive audits on the winner in any round, revealing the true utility of the winner in that round. We design a mechanism achieving $T$-independent $O(K^2)$ regret in social welfare while requesting $O(K^3 \log T)$ audits in expectation, where $K$ is the number of agents and $T$ is the number of rounds. We also show an $\Omega(K)$ lower bound on the regret and an $\Omega(1)$ lower bound on the number of audits when having low regret. Algorithmically, we show that incentive-compatibility can be mostly enforced with an accurate estimation of the winning probability of each agent under truthful reporting. To do so, we impose future punishments and introduce a *flagging* component, allowing agents to flag any biased estimate (we show that doing so aligns with individual incentives). On the technical side, without monetary transfers and distributional information, the central planner cannot ensure that truthful reporting is exactly an equilibrium. Instead, we characterize the equilibrium via a reduction to a simpler *auxiliary game*, in which agents cannot strategize until late in the $T$ rounds of the allocation problem. The tools developed therein may be of independent interest for other mechanism design problems in which the revelation principle cannot be readily applied. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.08412 |
| By: | Keisuke Bando; Kenzo Imamura; Yasushi Kawase |
| Abstract: | Choice correspondences are crucial in decision-making, especially when faced with indifferences or ties. While tie-breaking can transform a choice correspondence into a choice function, it often introduces inefficiencies. This paper introduces a novel notion of path-independence (PI) for choice correspondences, extending the existing concept of PI for choice functions. Intuitively, a choice correspondence is PI if any consistent tie-breaking produces a PI choice function. This new notion yields several important properties. First, PI choice correspondences are rationalizabile, meaning they can be represented as the maximization of a utility function. This extends a core feature of PI in choice functions. Second, we demonstrate that the set of choices selected by a PI choice correspondence for any subset forms a generalized matroid. This property reveals that PI choice correspondences exhibit a nice structural property. Third, we establish that choice correspondences rationalized by ordinally concave functions inherently satisfy the PI condition. This aligns with recent findings that a choice function satisfies PI if and only if it can be rationalized by an ordinally concave function. Building on these theoretical foundations, we explore stable and efficient matchings under PI choice correspondences. Specifically, we investigate constrained efficient matchings, which are efficient (for one side of the market) within the set of stable matchings. Under responsive choice correspondences, such matchings are characterized by cycles. However, this cycle-based characterization fails in more general settings. We demonstrate that when the choice correspondence of each school satisfies both PI and monotonicity conditions, a similar cycle-based characterization is restored. These findings provide new insights into the matching theory and its practical applications. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.09265 |
| By: | Dirk Bergemann; Michael C. Wang |
| Abstract: | We consider a seller who offers services to a buyer with multi-unit demand. Prior to the realization of demand, the buyer receives a noisy signal of their future demand, and the seller can design contracts based on the reported value of this signal. Thus, the buyer can contract with the service provider for an unknown level of future consumption, such as in the market for cloud computing resources or software services. We characterize the optimal dynamic contract, extending the classic sequential screening framework to a nonlinear and multi-unit setting. The optimal mechanism gives discounts to buyers who report higher signals, but in exchange they must provide larger fixed payments. We then describe how the optimal mechanism can be implemented by two common forms of contracts observed in practice, the two-part tariff and the committed spend contract. Finally, we use extensions of our base model to shed light on policy-focused questions, such as analyzing how the optimal contract changes when the buyer faces commitment costs, or when there are liquid spot markets. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.08022 |
| By: | Thomas H\"ubner; Gabriela Hug |
| Abstract: | A key challenge in combinatorial auctions is designing bid formats that accurately capture agents' preferences while remaining computationally feasible. This is especially true for electricity auctions, where complex preferences complicate straightforward solutions. In this context, we examine the XOR package bid, the default choice in combinatorial auctions and adopted in European day-ahead and intraday auctions under the name ``exclusive group of block bids''. Unlike parametric bid formats often employed in US power auctions, XOR package bids are technology-agnostic, making them particularly suitable for emerging demand-side participants. However, the challenge with package bids is that auctioneers must limit their number to maintain computational feasibility. As a result, agents are constrained in expressing their preferences, potentially lowering their surplus and reducing overall welfare. To address this issue, we propose decision support algorithms that optimize package bid selection, evaluate welfare losses resulting from bid limitations, and explore alternative bid formats. Our findings offer actionable insights for both auctioneers and bidders. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.09420 |
| By: | Zhiming Feng |
| Abstract: | The optimal bundling problem is the design of bundles (and prices) that maximize the expected virtual surplus, constrained by individual rationality and incentive compatibility. I focus on a relaxed, constraint-free problem that maximizes the expected virtual surplus with deterministic allocations. I show that when the difference of two virtual value functions for any pair of stochastic bundles is single-crossing, the minimal optimal menu for the relaxed problem is the set of all undominated bundles, where dominance refers to the natural comparison of virtual values across the type space. Under single-crossing differences, this comparison simplifies to comparisons on boundary types, enabling an algorithm to generate the minimal optimal menu. I further show that when the difference of two virtual value functions for any pair of stochastic bundles is monotonic, there exists an endogenous order among deterministic bundles. This order justifies that the minimal optimal menu for the relaxed problem is also optimal for the nonrelaxed problem. I also characterize the conditions under which consumers' valuation functions and distributions allow the virtual value functions to exhibit monotonic differences. This characterization, combined with the dominance notion, solves related bundling problems such as distributional robustness, bundling with additive values, and the optimality of pure, nested, and relatively novel, singleton-bundle menus. As a side result, I discover new properties of single crossing and monotonic differences in convex environments. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.07863 |
| By: | Arne Lauber; Christoph March; Marco Sahm |
| Abstract: | We conduct a laboratory experiment to compare the fairness and intensity of round-robin tournaments with three symmetric players, a single prize, and two alternative match formats. Matches are either organized as lottery contests or all-pay auctions. Whereas we confirm the theoretical prediction that tournaments are less fair if matches are organized as all-pay auctions, we reject the predicted difference in tournament intensity. Moreover, the reason for the reduced fairness of tournaments based on all-pay auctions is also at odds with theory. In the lab, such tournaments heavily disfavor (in payoff-terms) the player acting in the final two matches. The reason is the substantially weaker than predicted discouragement of this player when competing first against the loser of the first match. Subjects try to exploit a perceived negative psychological momentum in such situations but only manage to end up in a dissipation trap: an effort-intense, final-like last match which significantly reduces their payoffs. |
| Keywords: | sequential round-robin tournaments, lottery contest, all-pay auction, laboratory experiment, discouragement effect, dissipation trap |
| JEL: | C72 C91 D72 Z20 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11677 |
| By: | Frederic Koessler; Marco Scarsini; Tristan Tomala |
| Abstract: | This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian nonatomic games, using direct information structures and obedient strategies. The main results demonstrate full implementation in a class of games with positive cost externalities. Specifically, if the game admits a strictly convex potential in every state, then for every Bayes correlated equilibrium outcome with finite support and rational action distributions, there exists a direct information structure that implements this outcome under all equilibria. When the potential is only weakly convex, we show that all equilibria implement the same expected social cost. Additionally, all Bayes correlated equilibria, including those with infinite support or irrational action distributions, are approximately implemented. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.05920 |
| By: | Nizar Riane |
| Abstract: | This paper examines the recent reform of Morocco's public procurement market through the lens of Keynesian beauty contest theory. The reform introduces a mechanism akin to a guessing-the-average game, where bidders attempt to estimate a reference price, which in turn impacts bidding strategies. We utilize this setup to empirically test key hypotheses within auction theory, specifically the roles of common knowledge and bounded rationality. Our findings indicate potential manipulation risks under the current rules, suggesting that a shift to a median criterion could improve robustness and reduce the likelihood of manipulation. This work contributes to the broader understanding of strategic interactions in procurement and offers a foundation for future research on improving fairness and efficiency in public contract allocation. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.00883 |
| By: | Dirk Bergemann; Alessandro Bonatti; Alex Smolin |
| Abstract: | We develop an economic framework to analyze the optimal pricing and product design of Large Language Models (LLM). Our framework captures several key features of LLMs: variable operational costs of processing input and output tokens; the ability to customize models through fine-tuning; and high-dimensional user heterogeneity in terms of task requirements and error sensitivity. In our model, a monopolistic seller offers multiple versions of LLMs through a menu of products. The optimal pricing structure depends on whether token allocation across tasks is contractible and whether users face scale constraints. Users with similar aggregate value-scale characteristics choose similar levels of fine-tuning and token consumption. The optimal mechanism can be implemented through menus of two-part tariffs, with higher markups for more intensive users. Our results rationalize observed industry practices such as tiered pricing based on model customization and usage levels. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.07736 |
| By: | Matthew Stephenson; Andrew Miller; Xyn Sun; Bhargav Annem; Rohan Parikh |
| Abstract: | We study a fundamental challenge in the economics of innovation: an inventor must reveal details of a new idea to secure compensation or funding, yet such disclosure risks expropriation. We present a model in which a seller (inventor) and buyer (investor) bargain over an information good under the threat of hold-up. In the classical setting, the seller withholds disclosure to avoid misappropriation, leading to inefficiency. We show that trusted execution environments (TEEs) combined with AI agents can mitigate and even fully eliminate this hold-up problem. By delegating the disclosure and payment decisions to tamper-proof programs, the seller can safely reveal the invention without risking expropriation, achieving full disclosure and an efficient ex post transfer. Moreover, even if the invention's value exceeds a threshold that TEEs can fully secure, partial disclosure still improves outcomes compared to no disclosure. Recognizing that real AI agents are imperfect, we model "agent errors" in payments or disclosures and demonstrate that budget caps and acceptance thresholds suffice to preserve most of the efficiency gains. Our results imply that cryptographic or hardware-based solutions can function as an "ironclad NDA, " substantially mitigating the fundamental disclosure-appropriation paradox first identified by Arrow (1962) and Nelson (1959). This has far-reaching policy implications for fostering R&D, technology transfer, and collaboration. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.07924 |