理论论文

As shortages of essential resources become more frequent, high prices alone may fail to curb demand. We study power limits for residential electricity, which restrict household consumption rather than setting it to zero as in rolling blackouts. We show theoretically and empirically that power limits can deliver electricity savings equivalent to sizable blackouts while affecting fewer households. The mechanism works through selection of high users, creating distributional trade-offs that depend on whether limits are uniform or proportional to contracted power. This highlights the potential of smart meters to improve shortage management while preserving access to essential electricity services.

This paper studies the optimal combination of government grants that provide direct public funding to nonprofits and tax incentives that reduce the cost of charitable giving. When nonprofits face high fundraising costs to attract donors, tax incentives cannot fully replace grants, which remain part of the optimal funding policy. When fundraising costs are sufficiently low, a government that can tailor tax incentives across causes can finance some causes entirely through donations. However, when cause-specific tax differentiation is unavailable, grants remain necessary to accommodate differences in funding needs across causes. In a calibrated example, imposing a uniform tax treatment of donations across charitable causes raises the optimal share of nonprofit funding covered by grants from 0 to 60%.

A designer employs a dynamic protocol to elicit private information. Protocols produce a set of contextual privacy violations—information learned that may be superfluous given the context. A protocol is maximally contextually private if there is no protocol that produces a proper subset of the violations it produces, while implementing the choice rule. Contextual privacy violations arise when a choice rule makes some agents collectively, but not individually, pivotal. In auctions, designing for contextual privacy requires choosing an initial question posed to each agent and the order for querying agents. Ascending-join protocols are maximally contextually private for k-item Vickrey auctions. (JEL D44, D82)

We study a data provider's problem of optimally designing and selling marketing lists that enable a retailer with private types to access consumers with heterogeneous characteristics. When virtual values satisfy a particular form of convexity (named boundary dominance), under certain regularity conditions, the optimal mechanism comprises fully revealing marketing lists, irrespective of whether the retailer's types are vertically or horizontally ordered. Moreover, in the vertical case, the optimal mechanism allows a simple “fixed-price” implementation. In the horizontal case, it exhibits no-exclusion and rotation properties. Conversely, if boundary dominance is violated, the optimal mechanism may not be fully revealing. (JEL D82, L81, M31)

This paper studies bid rigging in auctions with bidder preselection. We develop a theoretical model to analyze the optimal behavior of partial bid-rigging cartels and show how commonly used two-stage auction formats, in which the first stage is used to preselect bidders, may be exploited. Based on our theoretical results, we construct a collusion marker reflecting the optimal cartel strategy and, using administrative data on public procurement auctions in Slovakia, we identify bidders suspected of collusion. We show that bidder preselection allows cartels to exclude competitive rivals and thereby increase procurement costs above what would be possible without preselection. (JEL D43, D44, H57, L12)

We consider many-to-many matching with contracts where each agent can sign multiple contracts with the same agent. In other words, the unitarity condition is not assumed in this model. We offer a weaker substitutability condition called substitutability across doctors, which is a generalization of unilateral substitutability. We show that if every hospital’s choice function satisfies substitutability across doctors and every doctor’s choice function is responsive, then a stable outcome exists. We establish this result by generalizing the cumulative offer process. Moreover, we propose an even weaker substitutability condition that incorporates observability of doctors’ contract offers during the algorithm. The same algorithm guarantees the existence of a stable outcome even when substitutability across doctors is replaced with the weaker condition. We additionally present a specific class of choice functions satisfying the weaker condition that can be applied to a temporary staffing market, particularly in which temp agencies may assign multiple temporary workers to each client.

We study optimal service allocation through queues when agents have homogeneous preferences and must be incentivized to enter and remain in the queue. The designer controls entry, exit, service priority, and information about queue priorities. Under a mild regularity condition, the optimal mechanism admits agents only up to a cutoff queue length, never removes admitted agents, serves them according to a first-come, first-served (FCFS) rule, and provides no information beyond recommendations. FCFS is also necessary for optimality in a rich domain. The result identifies a new role for queue disciplines in regulating agents’ beliefs and dynamic incentives, and uncovers a hitherto unrecognized virtue of FCFS in this regard.

We study the optimal auction design problem when bidders are ambiguity averse and follow the max-min expected utility model. Each bidder’s set of priors consists of beliefs that are close to the seller’s belief, where “closeness” is defined by a divergence. For a given allocation rule, we show that optimal transfers belong to a specific class of transfers, termed win-lose dependent transfers, in which bidders’ transfers upon winning and losing depend only on their own types but not on their opponents’ type reports. This result effectively reduces the infinite-dimensional problem of identifying an optimal transfer function into a two-dimensional problem of determining two constants-one for winning and another for losing. Solving this reduced problem, we show that among efficient mechanisms without transfers to losing bidders, the first-price auction is optimal, thereby outperforming other auction formats such as the second-price auction. We also discuss how the structure of the set of priors is related to the revenue ranking between the first- and second-price auctions.

We study priority-based matching markets with public and private endowments. We show that efficiency-adjusted deferred acceptance (EADA) is justified-envy minimal in the class of efficient mechanisms, while Top trading cycles (TTC) and other popular mechanisms are not. Our findings highlight EADA as an interesting alternative to TTC in the context of transplantation-organ markets. Restricting attention to strategyproof mechanisms, we show that TTC is justified-envy minimal, strengthening the result of Abdulkadiroglu et al. (2020).

In the context of one-to-one matching markets, we study myopic-farsighted stable sets, which are internally and externally stable when myopic agents consider immediate payoffs from their deviations, while farsighted agents anticipate counter-deviations and consider final payoffs. We constructively prove the existence of a (rational expectations) myopic-farsighted stable set, in which farsighted agents receive a single payoff while myopic agents may receive multiple payoffs. Our existence result extends to settings with enforcing coalitions of arbitrary size, yielding coalitional myopic-farsighted stable sets, and to settings where not all members of an enforcing coalition must strictly gain, yielding myopic-farsighted weakly stable sets. When all farsighted agents have unit demand, our results also extend to many-to-one matching markets. As a key corollary, we provide a foundation for the efficiency-adjusted deferred acceptance algorithm by showing that its outcome constitutes a singleton myopic-farsighted stable set when one side is farsighted and the other is myopic.

In school choice problems, the pursuit of student welfare (efficiency) is constrained by the requirement to respect schools’ priorities (fairness). Among fair matchings, even the welfare maximizing one, the Student-Optimal Stable Matching (SOSM), is inefficient. Moreover, any mechanism that yields welfare gains over the SOSM is manipulable by students. This paper investigates the fairness and incentive properties of efficient mechanisms. We compare matchings using the notion that one matching is less unfair than another if it generates a smaller set of students whose priorities are violated, and we define minimal unfairness accordingly. We show that the Efficiency-Adjusted Deferred Acceptance (EADA) mechanism is minimally unfair within the class of Pareto efficient mechanisms satisfying a simple incentive requirement, top-manipulation-proofness. Moreover, the EADA satisfies a stronger property, upper-manipulation-proofness. Upper-manipulation-proofness is a broad incentive property one can maintain while improving upon the SOSM. Together, these results highlight a sharp frontier in school choice: when the objective is efficiency and improving student welfare over the SOSM, the EADA emerges as a compelling mechanism in both fairness and incentive terms.

We consider a market with indivisible objects, called houses, and monetary transfers. Each house is initially occupied by one agent and each agent demands exactly one house. The problem is to identify the complete set of direct allocation mechanisms that can be used to reallocate the houses among the agents. On the one hand, for price eq1uilibrium mechanisms, we show that the only non-manipulable mechanism is one with a minimum equilibrium price vector. The result is not true on the classic or the quasi-linear domains, but on reduced domains of preference profiles containing “almost all” profiles in the classic or the quasi-linear domain, respectively. On the other hand, while minimum price equilibrium mechanisms are not necessarily efficient (as prices are not zero), we show that no non-manipulable mechanism Pareto dominates a minimum price equilibrium mechanism, making them constrained efficient in the class of non-manipulable mechanisms.

Abstract We introduce markup equilibrium—an extension of Walrasian equilibrium in which consumers pay a fixed percentage markup over producer prices. In quasilinear markets, markup equilibria exist despite nonconvexities. They are resource-feasible and envy-free, incur no budget deficit, and require little more communication and computation than ordinary Walrasian equilibrium. The associated markup mechanism is asymptotically incentive-compatible. We also introduce a Bound-Form First Welfare Theorem, which states that for any feasible allocation, the welfare loss compared to the first-best is bounded, using any price vector, by the sum of the resulting (i) budget surplus and (ii) rationing losses suffered by the participants. Using producer prices, this bound implies that any markup equilibrium with a small markup and few unallocated goods is nearly efficient.

In this article, we investigate how information about production externalities, such as ecolabels, can be presented to create market pressure on firms to reduce these externalities. Specifically, we explore whether integrating information on externalities with consumer product ratings into a single combined rating can generate pressure to reduce externalities from all consumers, not just environmentally conscious ones. Theoretically, we demonstrate the existence of an equilibrium where producers invest in both high product quality and low production externalities. We show that under separate ratings, this equilibrium depends on a high proportion of “green” consumers, whereas a combined rating achieves similar results without such a requirement. More broadly, our model suggests that bundling ratings can compel producers to address niche concerns more effectively. We experimentally validate this prediction across two studies, confirming that bundling ratings significantly increases producer investment in additional attributes, such as reducing externalities, while maintaining the rating system’s ability to incentivize high product quality.

“Superstar” markets, where a small portion of individuals earn disproportionately high incomes, are common in fields like entrepreneurship, sports, and entertainment. Participants in these markets face significant income uncertainty, which can deter entry or prompt early exit. To address this difficulty, we propose income pools: contracts where individuals agree to share a portion of future earnings with pool members if a specific salary milestone is achieved. To date, hundreds of income pool contracts have been signed in practice. This paper develops the first mathematical model to analyze such contracts, focusing on stability (i.e., pools where no agents leave or join). When constrained to creating a single pool, we show that a stable pool always exists with specific structural properties. Generally, stronger agents tend to be more “collaborative” and favor larger pools, whereas weaker agents are more “selfish” and prefer smaller pools. Next, we analyze pools that adhere to a maximum size (mirroring current practice) and show that stability persists. These pools typically require more weaker agents than strong ones and we find an interesting “Pareto dominance” result, whereby all agents in a stable pool prefer a particular unique stable pool. Finally, we study general partition structures, prove that a stable partition always exists under certain conditions, and provide an algorithm to construct such a partition. We conclude with a case study on data from 2,000 professional baseball players to demonstrate a 20%–30% increase in social welfare if players join income pools, under varying contract parameters.

Innovation contests incentivize the participants’ to exert effort toward combining (recombining) their existing knowledge to create solutions. In the current work, we consider the case of serial contests, where effort to create solutions for earlier contests can also expand the participant’s knowledge, which can then be valuable in future contests. We develop a novel framework that explicitly includes the generation and utilization of knowledge by participants in knowledge-driven serial innovation contests, and we analyze the implications of this framework for optimal incentive design. Analysis of our model reveals that the efforts expended by participants in a contest can depend on future rewards, especially when learning emerges as a “side effect” of execution effort (i.e., learning while doing). In fact, participants will exert effort in an earlier contest even when its associated reward is zero. In contrast, when explicit knowledge generation effort is feasible (i.e., learning before doing), the contest designer should increase the reward for the earlier contest to prevent participants from postponing their learning. Our model demonstrates that whether one should assign higher reward to the earlier or later contest depends on the mode of learning, the participant pool’s ex ante knowledge, and the transferability of learning from one contest to the next.

This paper introduces a second-price auction with a flexible reserve price, where the reserve price for the top bidder is not fixed but rather determined as a function of all losing bids. We show that when bidders are ex ante heterogeneous, a second-price auction with an optimally chosen flexible reserve price not only generates strictly higher expected revenue than that of a second-price auction with any fixed reserve price but is also revenue-maximizing among all mechanisms that implement discrimination-free social choice functions. We also provide an axiomatic characterization of all second-price auctions with a flexible reserve price. Finally, we discuss real-life implementation.

This paper investigates how autonomous vehicles (AVs) may reshape morning commute travel patterns and impact parking in a central business district (CBD). We develop a continuous-time game-theoretic traffic model that takes into account key economic deterrents to driving, such as parking fees and traffic congestion, and characterize the departure time and parking location (inside or outside the CBD parking area) patterns of commuters in equilibrium. Our analysis shows that all AV commuters may choose to park outside the CBD in equilibrium, increasing both vehicle hours and vehicle miles traveled as compared with the case with all human-driven vehicles. This change increases the total system cost and suggests a potential for CBD land use changes (e.g., repurposing CBD parking spots as commercial and residential areas) after the mass adoption of AVs. To reduce the total system cost, an urban planner may regulate commuters’ decisions by adjusting parking fees and/or imposing congestion tolls as a short-term measure, or adjusting infrastructure, for example, converting CBD parking spaces to drop-off spots for AVs. Our results indicate that these measures can reduce the total system cost substantially (e.g., up to 28.5% when calibrating our model to data from Pittsburgh).

We study the role of correlation in matching markets, where multiple decision makers simultaneously face selection problems from the same pool of candidates. We propose a model in which a candidate’s priority scores across different decision makers exhibit varying levels of correlation dependent on the candidate’s sociodemographic group. Such differential correlation can arise in school choice because of the varying prevalence of selection criteria, in college admissions because of test-optional policies, or because of algorithmic monoculture, that is, when decision makers rely on the same algorithms and data sets to evaluate candidates. We show that higher correlation for one of the groups generally improves the outcome for all groups, leading to higher efficiency. However, students from a given group are more likely to remain unmatched as their own correlation level increases. This implies that it is advantageous to belong to a low-correlation group. Finally, we extend the tie-breaking literature to multiple priority classes and intermediate levels of correlation. Overall, our results point to differential correlation as a previously overlooked systemic source of group inequalities in school, university, and job admissions. This paper was accepted by Itai Ashlagi, revenue management and market analytics. Funding: This work was partially supported by MIAI @ Grenoble Alpes [Grants ANR-19-P3IA-0003 and ANR-23-PEIA-0003], by the French National Research Agency (ANR) [Grants ANR-19-CE48-0018 and ANR-20-CE23-0007], and by the National Science Foundation [Grant DMS-1928930] and by the Alfred P. Sloan Foundation [Grant G-2021-16778], which funded B. Pradelski’s residency at the Simons Laufer Mathematical Sciences Institute (formerly MSRI) in Berkeley, CA, during the Fall 2023 semester. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.06067 .

Many large cities have adopted a policy of restricting the number of new vehicle licenses in order to address the challenges of traffic and air pollution problems. An important question that then arises is how to allocate these limited new license quotas among a large set of demanders while taking both social efficiency and equality into consideration. Inspired by this practical problem, we study the problem of designing simple and optimal mechanisms to tradeoff between efficiency and equality in a similar public goods allocation problem. We first propose a truthful two-group mechanism framework that is both general and simple and then use it to compute the optimal solution that maximizes social efficiency while guaranteeing a certain level of equality. Interestingly and surprisingly, under some natural conditions regarding the players’ private values, we show that the optimal mechanisms within the proposed framework are always the mechanisms that first run an auction and then run a lottery (ATL for short). In addition, beyond the framework and those conditions, we prove that the ATL mechanism can always guarantee at least $1-c+c^{2}$ ($c\in[0,1]$ is the minimum equality level) of the optimal solution efficiency. This approximation ratio can in practice be further improved to near-optimal when resources are scarce and the natural conditions hold. We further establish a theoretical connection between these natural conditions and common value distributions, demonstrating that these conditions are widely satisfied in practice. Finally, we implement several experiments to verify the ATL mechanism’s optimality and robustness.