Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
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We study how delegating pricing to large language models (LLMs) can facilitate collusion in a duopoly when both sellers rely on the same pre-trained model. The LLM is characterized by (i) a propensity parameter capturing its internal bias toward high-price recommendations and (ii) an output-fidelity parameter measuring how tightly outputs track that bias; the propensity evolves through retraining. We show that configuring LLMs for robustness and reproducibility can induce collusion via a phase transition: there exists a critical output-fidelity threshold that pins down long-run behavior. Below it, competitive pricing is the unique long-run outcome. Above it, the system is bistable, with competitive and collusive pricing both locally stable and the realized outcome determined by the model's initial preference. The collusive regime resembles tacit collusion: prices are elevated on average, yet occasional low-price recommendations provide plausible deniability. With perfect fidelity, full collusion emerges from any interior initial condition. For finite training batches of size $b$, infrequent retraining (driven by computational costs) further amplifies collusion: conditional on starting in the collusive basin, the probability of collusion approaches one as $b$ grows, since larger batches dampen stochastic fluctuations that might otherwise tip the system toward competition. The indeterminacy region shrinks at rate $O(1/\sqrt{b})$.
We present a new approach to formulating and solving heterogeneous agent models with aggregate risk. We replace the cross-sectional distribution with low-dimensional prices as state variables and let agents learn equilibrium price dynamics directly from simulated paths. To do so, we introduce a structural reinforcement learning (SRL) method which treats prices via simulation while exploiting agents' structural knowledge of their own individual dynamics. Our SRL method yields a general and highly efficient global solution method for heterogeneous agent models that sidesteps the Master equation and handles problems traditional methods struggle with, in particular nontrivial market-clearing conditions. We illustrate the approach in the Krusell-Smith model, the Huggett model with aggregate shocks, and a HANK model with a forward-looking Phillips curve, all of which we solve globally within minutes.
2512.10203We study Sybil manipulation in BRACE, a competitive equilibrium mechanism for combinatorial exchanges, by treating identity creation as a finite perturbation of the empirical distribution of reported types. Under standard regularity assumptions on the excess demand map and smoothness of principal utilities, we obtain explicit linear bounds on price and welfare deviations induced by bounded Sybil invasion. Using these bounds, we prove a sharp contrast: strategyproofness in the large holds if and only if each principal's share of identities vanishes, whereas any principal with a persistent positive share can construct deviations yielding strictly positive limiting gains. We further show that the feasibility of BRACE fails in the event of an unbounded population of Sybils and provide a precise cost threshold that ensures disincentivization of such attacks in large markets.
How should a buyer design procurement mechanisms when suppliers' costs are unknown, and the buyer does not have a prior belief? We demonstrate that simple mechanisms - that share a constant fraction of the buyer utility with the seller - allow the buyer to realize a guaranteed positive fraction of the efficient social surplus across all possible costs. Moreover, a judicious choice of the share based on the known demand maximizes the surplus ratio guarantee that can be attained across all possible (arbitrarily complex and nonlinear) mechanisms and cost functions. Similar results hold in related nonlinear pricing and optimal regulation problems.
2512.07798We study optimal auction design in an independent private values environment where bidders can endogenously -- but at a cost -- improve information about their own valuations. The optimal mechanism is two-stage: at stage-1 bidders register an information acquisition plan and pay a transfer; at stage-2 they bid, and allocation and payments are determined. We show that the revenue-optimal stage-2 rule is the Vickrey--Clarke--Groves (VCG) mechanism, while stage-1 transfers implement the optimal screening of types and absorb information rents consistent with incentive compatibility and participation. By committing to VCG ex post, the pre-auction information game becomes a potential game, so equilibrium information choices maximize expected welfare; the stage-1 fee schedule then transfers an optimal amount of payoff without conditioning on unverifiable cost scales. The design is robust to asymmetric primitives and accommodates a wide range of information technologies, providing a simple implementation that unifies efficiency and optimal revenue in environments with endogenous information acquisition.
2512.03930An axiomatic characterization of Nash equilibrium is provided for games in normal form. The Nash equilibrium correspondence is shown to be fully characterized by four simple and intuitive axioms, two of which are inspired by contraction and expansion consistency properties from the literature on abstract choice theory. The axiomatization applies to Nash equilibria in pure and mixed strategies alike, to games with strategy sets of any cardinality, and it does not require that players' preferences have a utility or expected utility representation.
In a paper published in The Economic Journal in 2000, Weisbuch et al.\ introduce a model for buyers' preferences to the various sellers in over-the-counter (OTC) fish markets. While this model has become an archetype of economic conceptualization that combines bounded rationality and myopic reasoning, the literature on its asymptotic behaviours has remained scarce. In this paper, we proceed to a mathematical analysis of the dynamics and its full characterization in the simplest case of homogeneous buyer populations. By using elements of the theory of cooperative dynamical systems, we prove that, independently of the number of sellers and parameters, for almost every initial condition, the subsequent trajectory must asymptotically approach a stationary state. Moreover, for simple enough distributions of the sellers' attractiveness, we determine all stationary states and their parameter-dependent stability. This analysis shows that in most cases, the asymptotic preferences are ordered as the attractiveness are. However, depending on the parameters, there also exist robust functioning modes in which those sellers with highest preference are not the ones that provide highest profit.
Traditional auction theory posits that bid value exhibits a positive correlation with the probability of securing the auctioned object in ascending auctions. However, under uncertainty and incomplete information, as is characteristic in real-time advertising markets, truthful bidding may not always represent a dominant strategy or yield a Pure Strategy Nash Equilibrium. Real-Time Bidding (RTB) platforms operationalize impression-level auctions via programmatic interfaces, where advertisers compete in first-price auction settings and often resort to bid shading, i.e., strategically submitting bids below their private valuations to optimize payoff. This paper empirically investigates bid shading behaviors and strategic adaptation using large-scale RTB auction data from the Yahoo Webscope dataset. Integrating Minority Game Theory with clustering algorithms and variance-scaling diagnostics, we analyze equilibrium bidding behavior across temporally segmented impression markets. Our results reveal the emergence of minority-based bidding strategies, wherein agents partition hourly ad slots into submarkets and place bids strategically where they anticipate being in the numerical minority. This strategic heterogeneity facilitates reduced expenditure while enhancing win probability, functioning as an endogenous bid shading mechanism. The analysis highlights the computational and economic implications of minority strategies in shaping bidder dynamics and pricing outcomes in decentralized, high-frequency auction environments.
We introduce a graph-theoretic framework based on discrete sheaves to diagnose and localize inconsistencies in preference aggregation. Unlike traditional linearization methods (e.g., HodgeRank), this approach preserves the discrete structure of ordinal preferences, identifying which specific voter interactions cause aggregation failure -- information that global methods cannot provide -- via the Obstruction Locus. We formalize the Incompatibility Index to quantify these local conflicts and examine their behavior under stochastic variations using the Mallows model. Additionally, we develop a rigorous sheaf-theoretic pushforward operation to model voter merging, implemented via a polynomial-time constraint DAG algorithm. We demonstrate that graph quotients transform distributed edge conflicts into local impossibilities (empty stalks), providing a topological characterization of how aggregation paradoxes persist across scales.
Our work investigates the economic efficiency of the prevailing "ladder-step" investment strategy in oil and gas exploration, which advocates for the incremental acquisition of geological information throughout the project lifecycle. By employing a multi-agent Deep Reinforcement Learning (DRL) framework, we model an alternative strategy that prioritizes the early acquisition of high-quality information assets. We simulate the entire upstream value chain-comprising competitive bidding, exploration, and development phases-to evaluate the economic impact of this approach relative to traditional methods. Our results demonstrate that front-loading information investment significantly reduces the costs associated with redundant data acquisition and enhances the precision of reserve valuation. Specifically, we find that the alternative strategy outperforms traditional methods in highly competitive environments by mitigating the "winner's curse" through more accurate bidding. Furthermore, the economic benefits are most pronounced during the development phase, where superior data quality minimizes capital misallocation. These findings suggest that optimal investment timing is structurally dependent on market competition rather than solely on price volatility, offering a new paradigm for capital allocation in extractive industries.
We study a continuous time contracting model in which a principal hires a risk averse agent to manage a project over a finite horizon and provides sequential payments whose timing is endogenously determined. The resulting nonzero-sum interaction between the principal and the agent is reformulated as a mixed control and stopping problem. Using numerical simulations, we investigate how factors such as the relative impatience of the parties and the number of bonus payments influence the principal's value and the structure of the optimal bonus payment scheme. A notable finding is that, in some contractual environments, the principal optimally offers a sign-on bonus to front-load incentives.
Electric power systems are increasingly turning to energy storage systems to balance supply and demand. But how much storage is required? What is the optimal volume of storage in a power system and on what does it depend? In addition, what form of hedge contracts do storage facilities require? We answer these questions in the special case in which the uncertainty in the power system involves successive draws of an independent, identically-distributed random variable. We characterize the conditions for the optimal operation of, and investment in, storage and show how these conditions can be understood graphically using price-duration curves. We also characterize the optimal hedge contracts for storage units.
This paper provides a unified approach to characterize the set of all feasible signals subject to privacy constraints. The Blackwell frontier of feasible signals can be decomposed into minimum informative signals achieving the Blackwell frontier of privacy variables, and conditionally privacy-preserving signals. A complete characterization of the minimum informative signals is then provided. We apply the framework to ex-post privacy (including differential and inferential privacy) and to constraints on posterior means of arbitrary statistics.
Originating in evolutionary game theory, the class of "zero-determinant" strategies enables a player to unilaterally enforce linear payoff relationships in simple repeated games. An upshot of this kind of payoff constraint is that it can shape the incentives for the opponent in a predetermined way. An example is when a player ensures that the agents get equal payoffs. While extensively studied in infinite-horizon games, extensions to discounted games, nonlinear payoff relationships, richer strategic environments, and behaviors with long memory remain incompletely understood. In this paper, we provide necessary and sufficient conditions for a player to enforce arbitrary payoff relationships (linear or nonlinear), in expectation, in discounted games. These conditions characterize precisely which payoff relationships are enforceable using strategies of arbitrary complexity. Our main result establishes that any such enforceable relationship can actually be implemented using a simple two-point reactive learning strategy, which conditions on the opponent's most recent action and the player's own previous mixed action, using information from only one round into the past. For additive payoff constraints, we show that enforcement is possible using even simpler (reactive) strategies that depend solely on the opponent's last move. In other words, this tractable class is universal within expectation-enforcing strategies. As examples, we apply these results to characterize extortionate, generous, equalizer, and fair strategies in the iterated prisoner's dilemma, asymmetric donation game, nonlinear donation game, and the hawk-dove game, identifying precisely when each class of strategy is enforceable and with what minimum discount factor.
2511.16357We study decentralized markets for goods whose utility perishes in time, with compute as a primary motivation. Recent advances in reproducible and verifiable execution allow jobs to pause, verify, and resume across heterogeneous hardware, which allow us to treat compute as time indexed capacity rather than bespoke bundles. We design an automated market maker (AMM) that posts an hourly price as a concave function of load--the ratio of current demand to a "floor supply" (providers willing to work at a preset floor). This mechanism decouples price discovery from allocation and yields transparent, low latency trading. We establish existence and uniqueness of equilibrium quotes and give conditions under which the equilibrium is admissible (i.e. active supply weakly exceeds demand). To align incentives, we pair a premium sharing pool (base cost plus a pro rata share of contemporaneous surplus) with a Cheapest Feasible Matching (CFM) rule; under mild assumptions, providers optimally stake early and fully while truthfully report costs. Despite being simple and computationally efficient, we show that CFM attains bounded worst case regret relative to an optimal benchmark.
A planner wants to select one agent out of n agents on the basis of a binary characteristic that is commonly known to all agents but is not observed by the planner. Any pair of agents can either be friends or enemies or impartials of each other. An individual's most preferred outcome is that she be selected. If she is not selected, then she would prefer that a friend be selected, and if neither she herself or a friend is selected, then she would prefer that an impartial agent be selected. Finally, her least preferred outcome is that an enemy be selected. The planner wants to design a dominant strategy incentive compatible mechanism in order to be able choose a desirable agent. We derive sufficient conditions for existence of efficient and DSIC mechanisms when the planner knows the bilateral relationships between agents. We also show that if the planner does not know these relationships, then there is no efficient and DSIC mechanism and we compare the relative efficiency of two ``second-best'' DSIC mechanisms. Finally, we obtain sharp characterization results when the network of friends and enemies satisfies structural balance.
Given the combined evidences of bounded rationality, limited information and short-term optimization, over-the-counter (OTC) fresh product markets provide a perfect instance where to develop a behavioural approach to the analysis of micro-economic systems. Aiming at characterizing via a rigorous mathematical analysis, the main features of the spontaneous organization and functioning of such markets, we introduce and we study a stylized dynamical model for the time evolution of buyers populations and prices/attractiveness at each wholesaler. The dynamics is governed by immediate reactions of the actors to changes in basic indicators. Buyers are influenced by some degree of loyalty to their regular suppliers. Yet, at times, they also prospect for potential better offers. On the other hand, sellers primarily aim at maximising their profit. Yet, they can be also prone to improving their competitiveness in case of clientele deficit. Our results reveal that, in spite of being governed by simple and immediate rules, the competition between sellers self-regulates in time, as it constrains to bounded ranges the dispersion of both prices and clientele volumes, does similarly for the mean clientele volume, and it generates oscillatory behaviours that prevent any seller to dominate permanently its competitors (and to be dominated forever). Long-term behaviours are also investigated, with focus on asymptotic convergence to an equilibrium, as can be expected for a standard functioning mode. In particular, in the simplest case of 2 competing sellers, a normal-form-like analysis proves that such convergence holds, provided that the buyer's loyalty is sufficiently high or the sellers' reactivity is sufficiently low. In other words, this result identifies and proves those characteristics of the system that are responsible for long term stability and asymptotic damping of the oscillations.
Apportionment refers to the well-studied problem of allocating legislative seats among parties or groups with different entitlements. We present a multi-level generalization of apportionment where the groups form a hierarchical structure, which gives rise to stronger versions of the upper and lower quota notions. We show that running Adams' method level-by-level satisfies upper quota, while running Jefferson's method or the quota method level-by-level guarantees lower quota. Moreover, we prove that both quota notions can always be fulfilled simultaneously.
2511.13736Classic Rock-Paper-Scissors, RPS, has seen many variants and generalizations in the past several years. In the previous paper, we defined playability and balance for games. We used these definitions to show that different forms of imbalance agree on the most balanced and least balanced form of playable two-player n-object RPS games, referred to as (2,n)-RPS. We reintroduce these definitions here and show that, given a conjecture, the generalization of this game for m<50 players is a strongly playable RPS game. We also show that this game maximizes these forms of imbalance in the limit as the number of players goes to infinity.
2511.03145We consider fair and consistent extensions of the Shapley value for games with externalities. Based on the restriction identified by Casajus et al. (2024, Games Econ. Behavior 147, 88-146), we define balanced contributions, Sobolev's consistency, and Hart and Mas-Colell's consistency for games with externalities, and we show that these properties lead to characterizations of the generalization of the Shapley value introduced by Macho-Stadler et al. (2007, J. Econ. Theory 135, 339-356), that parallel important characterizations of the Shapley value.
How should a buyer design procurement mechanisms when suppliers' costs are unknown, and the buyer does not have a prior belief? We demonstrate that simple mechanisms - that share a constant fraction of the buyer utility with the seller - allow the buyer to realize a guaranteed positive fraction of the efficient social surplus across all possible costs. Moreover, a judicious choice of the share based on the known demand maximizes the surplus ratio guarantee that can be attained across all possible (arbitrarily complex and nonlinear) mechanisms and cost functions. Similar results hold in related nonlinear pricing and optimal regulation problems.
We analyze a principal-agent procurement problem in which the principal (she) is unaware some of the marginal cost types of the agent (he). Communication arises naturally as some types of the agent may have an incentive to raise the principal's awareness (totally or partially) before a contract menu is offered. The resulting menu must not only reflect the principal's change in awareness, but also her learning about types from the agent's decision to raise her awareness in the first place. We capture this reasoning in a discrete concave model via a rationalizability procedure in which marginal beliefs over types are restricted to log-concavity, ``reverse'' Bayesianism, and mild assumptions of caution. We show that if the principal is ex ante only unaware of high-cost types, all of these types have an incentive raise her awareness of them -- otherwise, they would not be served. With three types, the two lower-cost types that the principal is initially aware of also want to raise her awareness of the high-cost type: Their quantities suffer no additional distortions and they both earn an extra information rent. Intuitively, the presence of an even higher cost type makes the original two look better. With more than three types, we show that this intuition may break down for types of whom the principal is initially aware of so that raising the principal's awareness could cease to be profitable for those types. When the principal is ex ante only unaware of more efficient (low-cost) types, then \textit{no type} raises her awareness, leaving her none the wiser.
The strategic choice of model "openness" has become a defining issue for the foundation model (FM) ecosystem. While this choice is intensely debated, its underlying economic drivers remain underexplored. We construct a two-period game-theoretic model to analyze how openness shapes competition in an AI value chain, featuring an incumbent developer, a downstream deployer, and an entrant developer. Openness exerts a dual effect: it amplifies knowledge spillovers to the entrant, but it also enhances the incumbent's advantage through a "data flywheel effect," whereby greater user engagement today further lowers the deployer's future fine-tuning cost. Our analysis reveals that the incumbent's optimal first-period openness is surprisingly non-monotonic in the strength of the data flywheel effect. When the data flywheel effect is either weak or very strong, the incumbent prefers a higher level of openness; however, for an intermediate range, it strategically restricts openness to impair the entrant's learning. This dynamic gives rise to an "openness trap," a critical policy paradox where transparency mandates can backfire by removing firms' strategic flexibility, reducing investment, and lowering welfare. We extend the model to show that other common interventions can be similarly ineffective. Vertical integration, for instance, only benefits the ecosystem when the data flywheel effect is strong enough to overcome the loss of a potentially more efficient competitor. Likewise, government subsidies intended to spur adoption can be captured entirely by the incumbent through strategic price and openness adjustments, leaving the rest of the value chain worse off. By modeling the developer's strategic response to competitive and regulatory pressures, we provide a robust framework for analyzing competition and designing effective policy in the complex and rapidly evolving FM ecosystem.
2508.02171Newfoundland and Labrador's municipalities face severe soft budget pressures due to narrow tax bases, high fixed service costs, and volatile resource revenues. We develop a Stackelberg style mechanism design model in which the province commits at t = 0 to an ex ante grant schedule and an ex post bailout rule. Municipalities privately observe their fiscal need type, choose effort, investment, and debt, and may receive bailouts when deficits exceed a statutory threshold. Under convexity and single crossing, the problem reduces to one dimensional screening and admits a tractable transfer mechanism with quadratic bailout costs and a statutory cap. The optimal ex ante rule is threshold-cap; under discretionary rescue at t = 2, it becomes threshold-linear-cap. A knife-edge inequality yields a self-consistent no bailout regime, and an explicit discount factor threshold renders hard budgets dynamically credible. We emphasize a class of monotone threshold signal rules; under this class, grant crowd out is null almost everywhere, which justifies the constant grant weight used in closed form expressions. The closed form characterization provides a policy template that maps to Newfoundland's institutions and clarifies the micro-data required for future calibration.
We study network revenue management problems motivated by applications such as railway ticket sales and hotel room bookings. Requests, each requiring a resource for a consecutive stay, arrive sequentially with known arrival probabilities. We investigate two scenarios: the accept-or-reject scenario, where a request can be fulfilled by assigning any available resource; and the BAM-based scenario, which generalizes the former by incorporating customer preferences through the basic attraction model (BAM), allowing the platform to offer an assortment of available resources from which the customer may choose. We develop polynomial-time policies and evaluate their performance using approximation ratios, defined as the ratio between the expected revenue of our policy and that of the optimal online algorithm. When each arrival has a fixed request type (e.g., the interval of the stay is fixed), we establish constant-factor guarantees: a ratio of 1 - 1/e for the accept-or-reject scenario and 0.25 for the BAM-based scenario. We further extend these results to the case where the request type is random (e.g., the interval of the stay is random). In this setting, the approximation ratios incur an additional multiplicative factor of 1 - 1/e, resulting in guarantees of at least 0.399 for the accept-or-reject scenario and 0.156 for the BAM-based scenario. These constant-factor guarantees stand in sharp contrast to the prior nonconstant competitive ratios that are benchmarked against the offline optimum.
We study learning in complete-information games, allowing the players' models of their environment to be misspecified. We introduce Berk--Nash rationalizability: the largest self-justified set of actions -- meaning each action in the set is optimal under some belief that is a best fit to outcomes generated by joint play within the set. We show that, in a model where players learn from past actions, every action played (or approached) infinitely often lies in this set. When players have a correct model of their environment, Berk--Nash rationalizability refines (correlated) rationalizability and coincides with it in two-player games. The concept delivers predictions on long-run behavior regardless of whether actions converge or not, thereby providing a practical alternative to proving convergence or solving complex stochastic learning dynamics. For example, if the rationalizable set is a singleton, actions converge almost surely.
This paper examines the market for AI models in which firms compete to provide accurate model predictions and consumers exhibit heterogeneous preferences for model accuracy. We develop a consumer-firm duopoly model to analyze how competition affects firms' incentives to improve model accuracy. Each firm aims to minimize its model's error, but this choice can often be suboptimal. Counterintuitively, we find that in a competitive market, firms that improve overall accuracy do not necessarily improve their profits. Rather, each firm's optimal decision is to invest further on the error dimension where it has a competitive advantage. By decomposing model errors into false positive and false negative rates, firms can reduce errors in each dimension through investments. Firms are strictly better off investing on their superior dimension and strictly worse off with investments on their inferior dimension. Profitable investments adversely affect consumers but increase overall welfare.
2502.06530This paper introduces a novel ranking of statistical experiments, the Linear-Blackwell (LB) order, equivalently characterized by (i) more dispersed posteriors and likelihood ratios in the sense of the linear convex order, (ii) a larger Lorenz zonoid--the set of statewise profiles spanned by signals, and (iii) greater variability of the posterior mean. We apply the LB order to compare experiments in binary-action decision problems and in problems with quasiconcave payoffs, as analyzed by Kolotilin, Corrao, and Wolitzky (2025). Furthermore, the LB order enables the comparison of experiments in moral hazard problems, complementing the findings in Holmström (1979) and Kim (1995). Finally, the LB order applies to the comparison of experiments generating ex post signals in screening problems.
2412.18628We study the problem of allocating the revenues raised via paid subscriptions to music streaming platforms among participating artists. We show that the main methods to solve streaming problems (pro-rata, user-centric and families generalizing them) can be seen as specific (well-known) rules to solve (multi-issue) claims problems. Our results permit to provide strong links between the well-established literature on claims problems and the emerging literature on streaming problems.
2411.07166We study an index to measure the popularity of artists in music streaming platforms. This index, which can be used to allocate the amount raised via paid subscriptions among participating artists, is based on the Shapley value, a centerpiece in cooperative game theory. We characterize this Shapley index combining several axioms formalizing principles with normative appeal. This permits to place the index in the literature, as an alternative to the well-known (and widely used in the industry) pro-rata and user-centric indices.
We study blockchain trade-intent auctions, which currently intermediate about USD 10 billion in trades each month. These auctions are combinatorial because executing multiple trade intents jointly generates additional efficiencies. However, the auctioneer cannot observe what each trader would have received had its order been auctioned individually and hence cannot determine how these efficiencies should be shared. We compare the two dominant mechanisms - batch auctions and simultaneous individual auctions - and introduce a novel definition of fairness applicable to combinatorial auctions. We then propose a fair combinatorial auction that endogenously constructs a fairness benchmark from individual bids and a counterfactual mechanism. Whether fairness guarantees arise in equilibrium depends on the counterfactual: all traders receive more in the equilibrium of the fair combinatorial auction than in the equilibrium of the counterfactual mechanism when the counterfactual is simultaneous first-price auctions, but that may not be the case if the counterfactual is simultaneous second-price auctions.
Budgetary constraints force organizations to pursue only a subset of possible innovation projects. Identifying which subset is most promising is an error-prone exercise, and involving multiple decision makers may be prudent. This raises the question of how to most effectively aggregate their collective nous. Our model of organizational portfolio selection provides some first answers. We show that portfolio performance can vary widely. Delegating evaluation makes sense when organizations employ the relevant experts and can assign projects to them. In most other settings, aggregating the impressions of multiple agents leads to better performance than delegation. In particular, letting agents rank projects often outperforms alternative aggregation rules -- including averaging agents' project scores as well as counting their approval votes -- especially when organizations have tight budgets and can select only a few project alternatives out of many.
2403.01442Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by each coalition. In the presence of externalities, coalition values can be defined through various approaches, notably by trying to determine the best and worst-case scenarios. Typically, the optimistic and pessimistic perspectives offer valuable insights into strategic interactions. In many applications, these approaches correspond to the coalition either choosing first or choosing after the complement coalition. In a general framework in which the actions of a group affects the set of feasible actions for others, we explore this relationship and show that it always holds in the presence of negative externalities, but only partly with positive externalities. We then show that if choosing first/last corresponds to these extreme values, we also obtain a useful inclusion result: allocations that do not allocate more than the optimistic upper bounds also do not allocate less than the pessimistic lower bounds. Moreover, we show that when externalities are negative, it is always possible to guarantee the non-emptiness of these sets of allocations. Finally, we explore applications to illustrate how our findings provide new results and offer a means to derive results from the existing literature.
The rapid advancement of generative AI is poised to disrupt the creative industry. Amidst the immense excitement for this new technology, its future development and applications in the creative industry hinge crucially upon two copyright issues: 1) the compensation to creators whose content has been used to train generative AI models (the fair use standard); and 2) the eligibility of AI-generated content for copyright protection (AI-copyrightability). While both issues have ignited heated debates among academics and practitioners, most analysis has focused on their challenges posed to existing copyright doctrines. In this paper, we aim to better understand the economic implications of these two regulatory issues and their interactions. By constructing a dynamic model with endogenous content creation and AI model development, we unravel the impacts of the fair use standard and AI-copyrightability on AI development, AI company profit, creators income, and consumer welfare, and how these impacts are influenced by various economic and operational factors. For example, while generous fair use (use data for AI training without compensating the creator) benefits all parties when abundant training data exists, it can hurt creators and consumers when such data is scarce. Similarly, stronger AI-copyrightability (AI content enjoys more copyright protection) could hinder AI development and reduce social welfare. Our analysis also highlights the complex interplay between these two copyright issues. For instance, when existing training data is scarce, generous fair use may be preferred only when AI-copyrightability is weak. Our findings underscore the need for policymakers to embrace a dynamic, context-specific approach in making regulatory decisions and provide insights for business leaders navigating the complexities of the global regulatory environment.
We study the problem of aggregating distributions, such as budget proposals, into a collective distribution. An ideal aggregation mechanism would be Pareto efficient, strategyproof, and fair. Most previous work assumes that agents evaluate budgets according to the $\ell_1$ distance to their ideal budget. We investigate and compare different models from the larger class of star-shaped utility functions - a multi-dimensional generalization of single-peaked preferences. For the case of two alternatives, we extend existing results by proving that under very general assumptions, the uniform phantom mechanism is the only strategyproof mechanism that satisfies proportionality - a minimal notion of fairness introduced by Freeman et al. (2021). Moving to the case of more than two alternatives, we establish sweeping impossibilities for $\ell_1$ and $\ell_\infty$ disutilities: no mechanism satisfies efficiency, strategyproofness, and proportionality. We then propose a new kind of star-shaped utilities based on evaluating budgets by the ratios of shares between a given budget and an ideal budget. For these utilities, efficiency, strategyproofness, and fairness become compatible. In particular, we prove that the mechanism that maximizes the Nash product of individual utilities is characterized by group-strategyproofness and a core-based fairness condition.
We study a three-layer data market comprising users (data owners), platforms, and a data buyer. Each user benefits from platform services in exchange for data, incurring privacy loss when their data, albeit noisily, is shared with the buyer. The user chooses platforms to share data with, while platforms decide on data noise levels and pricing before selling to the buyer. The buyer selects platforms to purchase data from. We model these interactions via a multi-stage game, focusing on the subgame Nash equilibrium. We find that when the buyer places a high value on user data (and platforms can command high prices), all platforms offer services to the user who joins and shares data with every platform. Conversely, when the buyer's valuation of user data is low, only large platforms with low service costs can afford to serve users. In this scenario, users exclusively join and share data with these low-cost platforms. Interestingly, increased competition benefits the buyer, not the user: as the number of platforms increases, the user utility does not necessarily improve while the buyer utility improves. However, increasing the competition improves the overall utilitarian welfare. Building on our analysis, we then study regulations to improve the user utility. We discover that banning data sharing maximizes user utility only when all platforms are low-cost. In mixed markets of high- and low-cost platforms, users prefer a minimum noise mandate over a sharing ban. Imposing this mandate on high-cost platforms and banning data sharing for low-cost ones further enhances user utility.
We consider a model of third-degree price discrimination where the seller's product valuation is unknown to the market designer, who aims to maximize buyer surplus by revealing buyer valuation information. Our main result shows that the regret is bounded by a $\frac{1}{e}$-fraction of the optimal buyer surplus when the seller has zero valuation for the product. This bound is attained by randomly drawing a seller valuation and applying the segmentation of Bergemann et al. (2015) with respect to the drawn valuation. We show that this bound is tight in the case of binary buyer valuation.
We study a sender-receiver model in which the receiver can commit to a decision rule before the sender determines the information policy. The decision rule can depend on the information structure chosen by the sender and the realized signals. This framework captures applications where a decision-maker (the receiver) seeks advice from an interested party (the sender). In these applications, the receiver frequently faces uncertainty regarding the sender's preferences and the set of feasible information structures. Consequently, we adopt a unified robust analysis framework that includes the max-min utility, the min-max regret, and the min-max competitive ratio as special cases. We show that the optimal decision rule is always a quota rule.
We develop a general framework for reserve systems that allocate scarce resources such as vaccines to unit-demand agents under prioritization and eligibility constraints, along with a computationally efficient mechanism. Reserve systems allocate scarce resources --such as vaccines, medical units, school seats, or government positions-- to essential groups by creating categories with prioritized beneficiaries. Prior work typically assumed a common baseline priority ordering and featured either hard or soft reserves. The threshold reserve model we introduce supports independent priority orderings, mixtures of hard and soft reserves, and overlapping categories, thereby capturing both beneficiary designations and eligibility constraints while offering policymakers greater flexibility. Our Iterative Max-in-Max Assignment Mechanism (IMMAM) satisfies all desirable properties in this domain: it respects priorities within categories, maximizes resource utilization, and then lexicographically maximizes beneficiary assignments. IMMAM is path independent and therefore well-behaved in settings with multiple institutions making simultaneous allocation decisions. We leverage path independence to obtain comparative statics and to significantly improve the mechanism's computational efficiency. We outline applications of our framework in the context of vaccine allocation.
2305.10286We consider the problem of funding public goods that are complementary in nature. Examples include charities handling different needs (e.g., protecting animals vs. providing healthcare), charitable donations to different individuals, or municipal units handling different issues (e.g., security vs. transportation). We model these complementarities by assuming Leontief preferences; that is, each donor seeks to maximize an individually weighted minimum of all contributions across the charities. Decentralized funding may be inefficient due to a lack of coordination among the donors; centralized funding may be undesirable as it ignores the preferences of individual donors. We present a mechanism that combines the advantages of both methods. The mechanism efficiently distributes each donor's contribution so that no subset of donors has an incentive to redistribute their donations. Moreover, it is group-strategyproof, satisfies desirable monotonicity properties, maximizes Nash welfare, returns a unique Lindahl equilibrium, and can be implemented via natural best-response spending dynamics.