理论论文

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.

We introduce the notion of preconvexity, which extends the familiar concept of convexity found in cooperative games with transferable utility. In a convex game, the larger the group joined by an agent, the larger the marginal value brought to the group by that agent. By contrast, in strictly preconvex games, an agent’s marginal contribution is initially decreasing (when joining small groups), and it eventually becomes increasing at (and above) some critical group size. As a consequence, the core of a preconvex game may be empty. Defining the property of semicohesiveness (related to marginal contributions at this critical group size), we prove that it is sufficient to guarantee a nonempty core. We also propose a new solution for the set of preconvex games; and we characterize this solution by combining three axioms which are natural in our framework. A stronger cohesiveness property (guaranteeing that our solution falls in the core) is also studied. Some additional results are provided for the special case of anticonvex games, for which marginal contributions are always non-increasing.

Faced with political opposition to efficient carbon pricing, climate policy resorts to alternative instruments, which come with welfare and fiscal costs of acceptability. To assess these costs, this study examines second-best policies combining a constant carbon tax with subsidies to carbon-free electricity generation and storage. Using a stylized dynamic model of the energy transition featuring fossil and clean energy sources and a carbon budget, we show that the lower the carbon tax, the greater the carbon pricing gap, and the larger the subsidies required to meet the carbon budget. Overaccumulation of clean capital may be needed to crowd out fossil fuels. Calibration to the European energy market reveals costs of acceptability up to 2.6% of welfare and a budget shortfall equivalent to 56% of the present value of electricity consumption. This suggests that relying on green subsidies for the energy transition may be unwise.

Most comparisons of preferences are instances of single-crossing dominance. We examine the lattice structure of single-crossing dominance, proving characterisation, existence and uniqueness results for minimum upper bounds of arbitrary sets of preferences. We apply these theorems to derive new comparative statics theorems for collective choice and under analyst uncertainty, and to characterise a general 'maxmin' class of uncertainty-averse preferences over Savage acts.

We introduce the family of games with intertemporal externalities, where two disjoint sets of players play sequentially. Coalitions formed by the present cohort generate worth today. Moreover, today’s partition of players exerts an externality on the future; the worth of a coalition formed by future players is influenced by this externality. We adapt the classic Shapley axioms and study their implications in our class of games. They do not suffice to single out a unique solution. We introduce two values using the interpretation of the Shapley value as the players’ expected contributions to coalitions: the one-coalition externality value and the naive value. We state a relationship between these values and the Shapley value of an associated game in characteristic function form. Our main results characterize the two values by adding one additional property to the classic Shapley axioms. A property of equal treatment of contributions leads to characterizing the one-coalition externality value. A property of equal treatment of externalities characterizes the naive value.

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.

When organizations adopt artificial intelligence (AI) to recognize individuals’ negative emotions and accordingly allocate limited resources, strategic users are incentivized to game the system by misrepresenting their emotions. The value of AI in automating such emotion-driven allocation may be undermined by gaming behavior, algorithmic noise in emotion detection, and the spillover effect of negative emotions. We develop a game-theoretical model to understand emotion AI adoption, particularly in customer care, and analyze the design of the associated allocation policies. We find that adopting emotion AI is valuable if the spillover effect of negative emotions is negligible compared with resource misallocation loss, regardless of algorithmic noise and gaming behavior. We also quantify the welfare impacts of emotion AI on the users, organization, and society. Notably, a stronger AI is not always socially desirable and regulation on emotion-driven allocation is needed. Finally, we characterize conditions under which leveraging the AI system is preferred to hiring human employees in emotion-driven allocation. We also explore the alternative application of using emotion AI to monitor strategic employees and compare it with hiring a human manager for monitoring. Intriguingly, algorithmic noise may increase the profit of AI monitoring. Our work provides implications for designing, adopting, and regulating emotion AI.

Growing political polarization has reshaped the business landscape, shifting the mix of private and public politics companies face and requiring managers to develop more sophisticated nonmarket strategies. Yet the literature has largely continued to study strategies aimed at public and private politics in isolation. We analyze repertoires of nonmarket strategies and how they evolve over time in a formal game theoretic model of the policy life cycle, providing an integrated framework for studying public and private politics. Industry may resist activist campaigns or concede to them and may also lobby to block legislation when public politics is viable. The evolution of public opinion in a polarized world divides the game into two distinct phases, an initial phase of pure private politics and a subsequent phase with both public and private politics. Polarization delays social consensus and intensifies activism while increasing industry resistance to it. As public concern about an issue rises over time, industry resistance to activist campaigns weakens, and lobbying becomes costlier and less likely. We reveal important complementarities between strategies: The ability to lobby in the latter phase makes industry more resistant to activist campaigns during both phases of the life cycle. Our analysis demonstrates clearly and precisely how suboptimal strategic decisions may result from a failure to fully coordinate nonmarket strategy instruments.

We examine a scenario in which an employee exerts productive effort to achieve a target but can also manipulate a performance measure to falsely claim target achievement. Although manipulation is detrimental from a societal perspective because of its negative externalities, the firm’s shareholders may benefit from undetected manipulation. We analyze the firm’s optimal implementation of internal control and its impact on the employee’s productive effort and manipulative behavior. We demonstrate that a profit-maximizing firm primarily utilizes internal control to enhance the employee’s performance pay contract; however, this does not necessarily reduce manipulation. We identify situations in which internal control reduces or aggravates manipulation and discuss factors that can complement internal control to combat manipulation.

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.

Choice models, which specify the consumers’ choice probabilities of options over a given choice set, are widely studied and applied in many fields. We propose a temporal tree representation of choice that covers all rational choice models. Compared with existing structural choice models, the tree representation exhibits two major advantages that address the key challenges of model identification. First, all rational choice models have a tree representation, and a subclass of tree representation (with set-dependent branching) has a one-to-one correspondence with the rational choice models. This bridges the gap in the existing characterizations of structural models, which are unidentifiable, impose uninterpretable conditions, or do not cover the entire space of rational choice models. Second, the tree representation allows for the flexibility of systematically specifying the choice model structure based on available knowledge and data. In particular, the number of parameters needed to specify a tree representation can be primarily determined by the sufficient knowledge level, which corresponds to a specific layer of the tree branching. The sufficient knowledge level can be empirically determined based on the amount of available data, which, in turn, determines the number of parameters needed for model estimation. Therefore, the tree representation allows for a natural way of data integration, avoiding misspecification from restrictive assumptions and overfitting for general models.

We model social media as collections of users producing and consuming content. Users value consuming content, but due to scarce attention, they may not value all content from other users. Users also value receiving attention, creating the incentive to attract an audience by producing valuable content but also through attention bartering—users mutually becoming each other’s audience. Attention bartering shapes substantially the patterns of production and consumption on social media, explains key features of social media behavior and platform decision making, and yields sharp predictions that are consistent with data we collect from #EconTwitter. We conduct Twitter and Instagram user surveys that yield additional direct evidence in support of attention bartering, and we discuss the implications of attention bartering for the design of social media platforms.

Risk pooling has become an increasingly critical tool for managing risks among corporations, institutions, states, and nations, with examples including multinational pooling, decentralized insurance schemes, catastrophe risk pooling, and burden sharing for nuclear accidents. Although there has been a rich literature on such practices, little is known from a theoretical viewpoint regarding the operational strategies of risk pools and, in particular, on issues about the effect of a pool’s expansion on each existing member’s welfare. This paper is the first to explore these issues by establishing different notions of consensus for the expansion of a risk pool: strong consensus, where both existing members and new candidates improve their risk measures due to the pool’s expansion, and weak consensus, which refers to the willingness of existing members to remain in the pool. Under optimal risk sharing for each pool, we show that its properties regarding expansion’s effects depend strongly on the underlying pricing rule. For instance, only with risk-adjusted equilibrium pricing are existing members willing to accept highly risky new members, whereas simple linear pricing excludes such members from the pool. Additionally, the impact of exogenous reinsurance on consensus is analyzed under both pricing rules. The established framework offers valuable managerial insights and policy implications, which we illustrate through two indicative case studies based on real data.

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.

We develop a generalized theory of rationed fertility to analyze treatment effect heterogeneity in the child quantity-quality trade-off. An exogenous increase in fertility can be either desired or undesired. We derive a positive rationing income effect on child quality for desired fertility increases but a negative rationing income effect for undesired fertility increases. We propose an econometric framework to identify treatment effects of desired and undesired fertility increases and estimate a structural model to gauge the quantitative importance of the novel rationing income effect. Our study highlights the importance of distinguishing between desired and undesired changes when evaluating social programs.