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on Economic Design |
| By: | Jingsheng Yu; Jun Zhang |
| Abstract: | We explore the core concept in a generalization of the housing market model where agents own fractional endowments while maintaining ordinal preferences. Recognizing that individuals are easier than coalitions to block an allocation, we adopt a definition in which individuals block an allocation if their received assignments do not first-order stochastically dominate their endowment, while a non-singleton coalition blocks an allocation if they can reallocate their endowments to obtain new assignments that first-order stochastically dominate their original assignments. Our findings show that, unlike the original model, the strong core may be empty, while the weak core is nonempty. The weak core always contains elements that satisfy equal treatment of equals, but it may not contain elements satisfying equal-endowment no envy. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.11151 |
| By: | Hu Fu; Tao Lin |
| Abstract: | In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding equilibrium notion -- Bayes Nash equilibria -- are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to designing better auction systems is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distribution of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $\tilde O(\frac{n}{\varepsilon^2})$ of samples from the bidders' value distributions. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies of bidders. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.02801 |
| By: | Saeed Alaei; Shuchi Chawla; Zhiyi Huang; Ali Makhdoumi; Azarakhsh Malekian |
| Abstract: | We consider a mechanism design setting with a single item and a single buyer who is uncertain about the value of the item. Both the buyer and the seller have a common model for the buyer's value, but the buyer discovers her true value only upon receiving the item. Mechanisms in this setting can be interpreted as randomized refund mechanisms, which allocate the item at some price and then offer a (partial and/or randomized) refund to the buyer in exchange for the item if the buyer is unsatisfied with her purchase. Motivated by their practical importance, we study the design of optimal deterministic mechanisms in this setting. We characterize optimal mechanisms as virtual value maximizers for both continuous and discrete type settings. We then use this characterization, along with bounds on the menu size complexity, to develop efficient algorithms for finding optimal and near-optimal deterministic mechanisms. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.04148 |
| By: | Shashwat Khare; Souvik Roy |
| Abstract: | We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions' preferences over sets of individuals are assumed to satisfy responsiveness, whereas couples' preferences over pairs of institutions may violate responsiveness. In this setting, we first assume that all institutions share a common preference ordering over individuals, and we establish: (i) a complete characterization of all couples' preference profiles for which a stable matching exists, under the additional assumption that couples violate responsiveness only to ensure co-location at the same institution, and (ii) a necessary and sufficient condition on the common institutional preference such that a stable matching exists when couples may violate responsiveness arbitrarily. Next, we relax the common preference assumption, requiring institutions to share a common ranking only over the members of each couple. Under this weaker assumption, we provide: (i) a complete characterization of all couples' preferences for which a stable matching exists, and (ii) a sufficient condition on individuals' preferences that guarantees the existence of a stable matching. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.07490 |
| By: | Yasunori Okumura |
| Abstract: | This paper studies general multi-unit probabilistic assignment problems involving indivisible objects, with a particular focus on achieving the fundamental fairness notion known as equal treatment of equals (ETE) and ensuring various notions of efficiency. We extend the definition of ETE so that it accommodates a variety of constraints and applications. We analyze the ETE reassignment procedure, which transforms any assignment into one satisfying ETE, and examine its compatibility with three efficiency concepts: ex-post efficiency, ordinal efficiency, and rank-minimizing efficiency. We show that while the ETE reassignment of an ex-post efficient assignment remains ex-post efficient, it may fail to preserve ordinal efficiency in general settings. However, since the ETE reassignment of a rank-minimizing assignment preserves rank-minimizing efficiency, the existence of assignments satisfying both ETE and ordinal efficiency can be established. Furthermore, we propose a computationally efficient method for constructing assignments that satisfy both ETE and ordinal efficiency under general upper bound constraints, by combining the serial dictatorship rule with appropriately specified priority lists and an ETE reassignment. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.14522 |
| By: | Patrick Lederer |
| Abstract: | Social decision schemes (SDSs) map the voters' preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (1977) has characterized the set of SDSs that are strategyproof with respect to all utility functions and his result implies that all such SDSs are either unfair to the voters or alternatives, or they require a significant amount of randomization. To circumvent this negative result, we propose the notion of $U$-strategyproofness which postulates that only voters with a utility function in a predefined set $U$ cannot manipulate. We then analyze the tradeoff between $U$-strategyproofness and various decisiveness notions that restrict the amount of randomization of SDSs. In particular, we show that if the utility functions in the set $U$ value the best alternative much more than other alternatives, there are $U$-strategyproof SDSs that choose an alternative with probability $1$ whenever all but $k$ voters rank it first. On the negative side, we demonstrate that $U$-strategyproofness is incompatible with Condorcet-consistency if the set $U$ satisfies minimal symmetry conditions. Finally, we show that no ex post efficient and $U$-strategyproof SDS can be significantly more decisive than the uniform random dictatorship if the voters are close to indifferent between their two favorite alternatives. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16195 |
| By: | Nikhil Garg |
| Abstract: | A core ethos of the Economics and Computation (EconCS) community is that people have complex private preferences and information of which the central planner is unaware, but which an appropriately designed mechanism can uncover to improve collective decisionmaking. This ethos underlies the community's largest deployed success stories, from stable matching systems to participatory budgeting. I ask: is this choice and information aggregation ``worth it''? In particular, I discuss how such systems induce \textit{heterogeneous participation}: those already relatively advantaged are, empirically, more able to pay time costs and navigate administrative burdens imposed by the mechanisms. I draw on three case studies, including my own work -- complex democratic mechanisms, resident crowdsourcing, and school matching. I end with lessons for practice and research, challenging the community to help reduce participation heterogeneity and design and deploy mechanisms that meet a ``best of both worlds'' north star: \textit{use preferences and information from those who choose to participate, but provide a ``sufficient'' quality of service to those who do not.} |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.03600 |
| By: | Xinli Guo |
| Abstract: | We study soft budget constraints in multi-tier public finance when an upper-tier government uses two instruments: an ex-ante grant schedule and an ex-post rescue. Under convex rescue costs and standard primitives, the three-stage leader-follower problem collapses to one dimensional screening with a single allocation index: the cap on realized rescue. A hazard-based characterization delivers a unified rule that nests (i) no rescue, (ii) a threshold-cap with commitment, and (iii) a threshold--linear--cap without commitment. The knife-edge for eliminating bailouts compares the marginal cost at the origin to the supremum of a virtual weight, and the comparative statics show how greater curvature tightens caps while discretion shifts transfers toward front loading by lowering the effective grant weight. The framework provides a portable benchmark for mechanism design and yields testable implications for policy and empirical work on intergovernmental finance. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10724 |
| By: | Agustin G. Bonifacio; Maria Haydee Fonseca-Mairena; Pablo Neme |
| Abstract: | We study coalition formation problems in the presence of externalities, focusing on settings where agents exhibit myopic expectations, that is, they evaluate potential deviations based solely on the immediate outcome, assuming no further reactions or reorganization by others. First, we establish a sufficient condition for the non-emptiness of both the core and the stable set. In the case of the core, our condition for ensuring non-emptiness also provides a characterization of all core partitions. We then turn our attention to problems with order-preserving preferences. Under our sufficient condition, the core and the stable set not only exist but also coincide, and convergence to a stable outcome is guaranteed. Furthermore, using the notion of absorbing set, we draw a connection between problems with order-preserving preferences and those without externalities. This allows us to lift known core non-emptiness results from the latter setting to the former, thereby establishing a novel bridge between these two classes of problems. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.03259 |
| By: | Souvik Roy; Agamani Saha |
| Abstract: | This paper explores a novel extension of dynamic matching theory by analyzing a three-way matching problem involving agents from three distinct populations, each with two possible types. Unlike traditional static or two-way dynamic models, our setting captures more complex team-formation environments where one agent from each of the three populations must be matched to form a valid team. We consider two preference structures: assortative or homophilic, where agents prefer to be matched with others of the same type, and dis-assortative or heterophilic, where diversity within the team is valued. Agents arrive sequentially and face a trade-off between matching immediately or waiting for a higher quality match in the future albeit with a waiting cost. We construct and analyze the corresponding transition probability matrices for each preference regime and demonstrate the existence and uniqueness of stationary distributions. Our results show that stable and efficient outcomes can arise in dynamic, multi-agent matching environments, offering a deeper understanding of how complex matching processes evolve over time and how they can be effectively managed. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.06126 |
| By: | Patrick Lederer |
| Abstract: | In rank aggregation, the task is to aggregate multiple weighted input rankings into a single output ranking. While numerous methods, so-called social welfare functions (SWFs), have been suggested for this problem, all of the classical SWFs tend to be majoritarian and are thus not acceptable when a proportional ranking is required. Motivated by this observation, we will design SWFs that guarantee that every input ranking is proportionally represented by the output ranking. Specifically, our central fairness condition requires that the number of pairwise comparisons between candidates on which an input ranking and the output ranking agree is proportional to the weight of the input ranking. As our main contribution, we present a simple SWF called the Proportional Sequential Borda rule, which satisfies this condition. Moreover, we introduce two variants of this rule: the Ranked Method of Equal Shares, which has a more utilitarian flavor while still satisfying our fairness condition, and the Flow-adjusting Borda rule, which satisfies an even stronger fairness condition. Many of our axioms and techniques are inspired by results on approval-based committee voting and participatory budgeting, where the concept of proportional representation has been studied in depth. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16177 |
| By: | Förster, Manuel (Center for Mathematical Economics, Bielefeld University); Närmann, Fynn Louis (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study a dynamic game in which a monopolistic seller sequentially discloses information about a binary state to a consumer through priced experiments. The consumer privately observes a binary signal which influences her willingness to pay for information. We show that if buyer types favor different actions but their willingness to pay for a state-revealing test is sufficiently close, then the seller can commit to a sequence of priced experiments that extracts the entire surplus of both consumer types simultaneously. The optimal sequence of experiments is such that the high-valuation type assigns a higher probability to outcomes that trigger further information acquisition, thus creating a difference in expected costs. As a key element of the construction, we introduce an ‘encryption protocol’ under which the consumer faces a stopping problem. We then characterize situations in which the seller strictly benefits from a dynamic selling strategy when perfect price discrimination is not feasible. Finally, we illustrate our framework in the context of medical diagnostic testing, showing that a free test followed by a state-revealing test is often sufficient to improve revenue in comparison with a static approach. |
| Keywords: | Information design, dynamic mechanism, selling information, encryption, price discrimination |
| Date: | 2025–07–03 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:749 |
| By: | Soheil Ghili; K. Sudhir; Nitish Jain; Ankur Garg |
| Abstract: | We build on theoretical results from the mechanism design literature to analyze empirical models of second-degree price discrimination (2PD). We show that for a random-coefficients discrete choice ("BLP") model to be suitable for studying 2PD, it must capture the covariance between two key random effects: (i) the "baseline" willingness to pay (affecting all product versions), and (ii) the perceived differentiation between versions. We then develop an experimental design that, among other features, identifies this covariance under common data constraints in 2PD environments. We implement this experiment in the field in collaboration with an international airline. Estimating the theoretically motivated empirical model on the experimental data, we demonstrate its applicability to 2PD decisions. We also show that test statistics from our design can enable qualitative inference on optimal 2PD policy even before estimating a demand model. Our methodology applies broadly across second-degree price discrimination settings. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.13426 |
| By: | Edith Elkind; Tzeh Yuan Neoh; Nicholas Teh |
| Abstract: | We study a temporal voting model where voters have dynamic preferences over a set of public chores -- projects that benefit society, but impose individual costs on those affected by their implementation. We investigate the computational complexity of optimizing utilitarian and egalitarian welfare. Our results show that while optimizing the former is computationally straightforward, minimizing the latter is computationally intractable, even in very restricted cases. Nevertheless, we identify several settings where this problem can be solved efficiently, either exactly or by an approximation algorithm. We also examine the effects of enforcing temporal fairness and its impact on social welfare, and analyze the competitive ratio of online algorithms. We then explore the strategic behavior of agents, providing insights into potential malfeasance in such decision-making environments. Finally, we discuss a range of fairness measures and their suitability for our setting. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.08810 |
| By: | Ivan Geffner; Caspar Oesterheld; Vincent Conitzer |
| Abstract: | We examine normal-form games in which players may \emph{pre-commit} to outcome-contingent transfers before choosing their actions. In the one-shot version of this model, Jackson and Wilkie showed that side contracting can backfire: even a game with a Pareto-optimal Nash equilibrium can devolve into inefficient equilibria once unbounded, simultaneous commitments are allowed. The root cause is a prisoner's dilemma effect, where each player can exploit her commitment power to reshape the equilibrium in her favor, harming overall welfare. To circumvent this problem we introduce a \emph{staged-commitment} protocol. Players may pledge transfers only in small, capped increments over multiple rounds, and the phase continues only with unanimous consent. We prove that, starting from any finite game $\Gamma$ with a non-degenerate Nash equilibrium $\vec{\sigma}$, this protocol implements every welfare-maximizing payoff profile that \emph{strictly} Pareto-improves $\vec{\sigma}$. Thus, gradual and bounded commitments restore the full efficiency potential of side payments while avoiding the inefficiencies identified by Jackson and Wilkie. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.07147 |
| By: | Hans Gersbach; Arthur Schichl; Oriol Tejada |
| Abstract: | Which level of voting costs is optimal in a democracy? This paper argues that intermediate voting costs - what we term a "Midcost democracy" - should be avoided, as they fail to ensure that electoral outcomes reflect the preferences of the majority. We study a standard binary majority decision in which a majority of the electorate prefers alternative A over alternative B. The population consists of partisan voters, who always participate, and non-partisan voters, who vote only when they believe their participation could be pivotal, given that voting entails a cost. We show that the probability of the majority-preferred alternative A winning is non-monotonic in the level of voting costs. Specifically, when voting costs are either high or negligible, alternative A wins in all equilibria. However, at intermediate cost levels, this alignment breaks down. These findings suggest that democratic systems should avoid institutional arrangements that lead to moderate voting costs, as they may undermine the majority principle. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.07300 |
| By: | Ali Aouad; Jingwei Ji; Yaron Shaposhnik |
| Abstract: | The Pandora's box problem (Weitzman 1979) is a core model in economic theory that captures an agent's (Pandora's) search for the best alternative (box). We study an important generalization of the problem where the agent can either fully open boxes for a certain fee to reveal their exact values or partially open them at a reduced cost. This introduces a new tradeoff between information acquisition and cost efficiency. We establish a hardness result and employ an array of techniques in stochastic optimization to provide a comprehensive analysis of this model. This includes (1) the identification of structural properties of the optimal policy that provide insights about optimal decisions; (2) the derivation of problem relaxations and provably near-optimal solutions; (3) the characterization of the optimal policy in special yet non-trivial cases; and (4) an extensive numerical study that compares the performance of various policies, and which provides additional insights about the optimal policy. Throughout, we show that intuitive threshold-based policies that extend the Pandora's box optimal solution can effectively guide search decisions. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.07508 |
| By: | Zizhe Xia |
| Abstract: | I study whether and which expert incentives can be provided at what cost when the states of the world become non-contractible, but there is some noisy observation about the states that can be contracted upon. A principal hires an agent to acquire costly information about the states, but it is not possible to pay the agent based on the realized states. Instead, the principal has access to a noisy (Blackwell) experiment about the states, and can pay bonuses based on its realization. The agent is risk neutral and protected by limited liability. I completely characterize what the principal can incentivize the agent to learn, and how to design contracts to minimize the costs to provide such incentives. I then study which contractible information is always better at incentive provision. This gives rise to a novel order on information. In the binary-binary case, this order is characterized by larger differences in the likelihood ratios of the two realizations. My results provide insights into what information is better for evaluating expert predictions. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10170 |
| By: | Roy, Nicholas (Resources for the Future); Burtraw, Dallas (Resources for the Future) |
| Abstract: | This issue brief examines how a small reform to the California carbon market could improve affordability by delivering billions of dollars to harden infrastructure, advance climate goals, and improve affordability in California. This reform kicks in only when allowance prices are low, harvesting emissions reductions when they are low cost.The state’s most impactful efforts to reduce greenhouse gas emissions have been sector-specific policies such as building standards, vehicle efficiency standards, the renewable portfolio standard, and other measures. In this context, the cap-and-trade program contributes a numerical carbon budget for covered sectors and generates revenues to the Greenhouse Gas Reduction Fund to fund investments.The cap-and-trade program also improves affordability by lowering cost.Although sector-specific policies have been effective in driving emissions reductions, the average cost per ton reduced by these policies has typically been greater than the cost of emissions reductions under the cap-and-trade program, as identified by the price of an emissions allowance. For instance, the 2022 Scoping Plan estimated average annual cost (2022-2035) per ton of emissions reductions under most regulatory measures would be multiple times greater than the price of an emissions allowance, which represents the marginal cost of emissions reductions motivated by the carbon market. An exception is the zero-emissions vehicle standard, another market-based mechanism, and measures to reduce vehicle miles traveled, which have negative costs.In other words, every emissions reduction motivated by the carbon market represents a cost savings for California.A reform that would further improve the cost effectiveness of California’s climate policy portfolio is the introduction of an Emissions Containment Reserve (ECR), which we describe below, and which exists in other robust carbon markets. We find that in 2023-24, improved market design through the introduction of an Emissions Containment Reserve would have collected nearly $1.5 billion in benefits for ratepayers and the state’s Greenhouse Gas Reduction Fund.An ECR would improve the contribution of emissions reductions from the cap-and-trade program in accelerating decarbonization of the state’s economy and boost ratepayer climate dividend and to the state’s Greenhouse Gas Reduction Fund. Moreover, this feature would be triggered only when allowance prices are low and when emissions reductions driven by the carbon market are less expensive than sector specific regulation, contributing in multiple ways to affordability in California. We identify several other benefits of an Emissions Containment Reserve including better alignment of the carbon market with the state’s overall climate policy portfolio, and reduced market uncertainty. |
| Date: | 2025–01–27 |
| URL: | https://d.repec.org/n?u=RePEc:rff:ibrief:ib-25-03 |