How can we design a market of human-generated content for use in training AI models that both enables technological progress and preserves individual incentives for high-quality content creation? Existing approaches take polar positions: a "free-for-all" model based on fair use and a "strong intellectual property rights" model. We show that both fail: Free-for-all does not compensate creators, and -- by modeling as a static Stackelberg game -- strong intellectual property rights also underpower creative incentives. We find this especially true for more innovative creators, a phenomenon we term the "originality penalty." Extending this insight to a dynamic model, we find another market failure undermining AI model performance, even for an initially good model: Such a model induces greater reliance by humans on AI-assisted creation, resulting in homogenized content feeding back into training, which degrades the model performance -- a "curse of precision." We further propose a market design with a data intermediary internalizing cross-creator externalities and subsidizing innovative contributions, thereby restoring efficiency.

Bandit models typically begin with arms, states, rewards, and transition rules. This paper instead begins with preferences over stopped local contingent schedules: possible unfoldings of a responsibility, project, experiment, or opportunity in its own local time. Behavioral axioms on single schedules characterize a generalized stopping representation with current utility, local discounting, and a broad continuation aggregator. A common-tail compensation axiom then allows calendar time to be priced across schedules. Imposing a tight elapsed-calendar constraint generates a rested generalized bandit and yields index optimality: the index is the shadow price of advancing a local clock. Expected-utility, learning, robust, rank-dependent, Choquet, and Pandora models arise as special cases.

Aumann defined common knowledge mathematically and established his now famous Agreement Theorem. We present a novel approach to quantifying how close individuals are to commonly knowing events, $(\delta,\epsilon)$-common knowledge, which is defined for any (and not just countable) probability spaces, and provide quantitative versions of the key results in this field. Specifically, we do this for Aumann's Agreement Theorem and Nielsen's extension thereof to random variables, as well as for the setting in which posteriors are communicated back and forth between individuals. Our results apply in particular to noisy communication settings.

This paper proposes an epistemic foundation for aggregating sets of probabilistic beliefs by retaining only shared beliefs. It develops a model of belief formation under information-acquisition costs and capacity constraints. In this model, different information technologies rationalize different belief-aggregation rules, such as the familiar linear, geometric, power, and multiplicative pooling. Since the ranking of uncertain policies depends on these aggregation rules, failing to base collective beliefs on the underlying technologies can cause welfare losses. An application to financial markets demonstrates how these technologies translate conflicting beliefs into equilibrium prices.

We study the problem of fair division of indivisible goods with constraints imposed by a prescribed independence structure, that is, a family of subsets of goods closed under taking subsets. As a motivating example, imagine that the goods to be divided are the available connections in a logistic, financial, or social network. The admissible bundle of goods for each agent must correspond to an acyclic set of edges, corresponding to a basic feasible solution to a linear network problem to be solved. Suppose that all agents assign the same value to each good (in the example, the network connections are equally important for every agent) and evaluate each bundle by summing the values of its goods. Is there a fair partition of the goods into such acyclic bundles? Surprisingly, the answer is yes, provided that the number of agents is at least the arboricity of $G$, and the fairness requirement is envy-freeness up to one good (EF1). The situation becomes more mysterious when agents have arbitrary additive valuations. Our main result guarantees that, in this case, epistemic EF1 partitions always exist, which means that each agent receives an acyclic bundle for which there exists a feasible partition of the remaining goods into acyclic bundles that they do not envy up to one good. We derive this conclusion from a general result for abstract independence structures defined on the sets of goods. We also discuss connections with several conjectures concerning matroids. In particular, we prove that any Hamiltonian matroid partitionable into two independent sets admits an EF1 bipartition with respect to a common monotone valuation. We complement our results with a constructive perspective: we present explicitly two algorithms for computing the fair allocations described above. Finally, we provide illustrative examples to demonstrate these algorithms on specific instances.

The Price of Anarchy (PoA) is a popular measure of the costs of decentralization in terms of efficiency losses. Almost all PoA analyses operate within a framework assuming both Cardinal Full-Comparability (CFC) and smoothness, in which case any derived bounds conveniently extend beyond pure Nash to coarse correlated equilibria and no-regret learning outcomes. However, interpersonal utility comparability is an additional assumption that generally has to be justified. Without it, cardinal utilities (e.g. defined under classical von Neumann--Morgenstern framework) are unique only up to agent-specific affine transformations, rendering both the utilitarian PoA and the classical smoothness conditions representation-dependent. In this paper, we operate under a more general Cardinal Non-Comparability (CNC) framework, under which the weighted Nash welfare is a canonical admissible aggregator. We introduce multiplicative smoothness, a product-form condition matched to the multiplicative structure of Nash welfare, and obtain PoA bounds that are CNC-invariant and extend to coarse correlated equilibria. We demonstrate applicability of our framework on single-choice welfare games, deriving the bounds through simple proof relying on multiplicative retention envelope and geometric closure. The interpretation of this bound in terms of the true cost of decentralization depends crucially on interpersonal comparability of utilities.

We study global uniqueness of competitive equilibrium in two-good pure-exchange economies with heterogeneous impatience types and a common HARA Bernoulli utility. The paper connects the CRRA sorting result of \citet{GeanakoplosWalsh2018} with the line of HARA uniqueness results developed in \citet{LoiMatta2022,LoiMatta2024}. In the CRRA case, ordered endowments provide a sorting mechanism for uniqueness. In the HARA case, uniqueness is known to hold for arbitrary endowments under the curvature bound $\gamma\le I/(I-1)$, where $I$ is the number of impatience types. For two types, the curvature restriction can be removed under a monotone sorting condition linking patience and endowment composition. The present paper shows that this high-curvature HARA sorting mechanism is not specific to the two-type case. Our main result proves global uniqueness for any finite number of impatience types and any $\gamma>1$. If types can be ordered so that more patient agents hold weakly more of the first good and weakly less of the second, then the equilibrium price is globally unique. Thus the paper extends the two-type high-curvature HARA result to a genuinely multi-type setting and complements the arbitrary-endowment low-curvature result by replacing the low-curvature restriction with an economically interpretable sorting restriction. In the CRRA subcase ($b=0$), the ordered-endowment condition coincides with that of \citet{GeanakoplosWalsh2018}, and our corollary recovers their uniqueness result. The contribution of the present paper is therefore not the sorting condition itself but its reach: the same ordered heterogeneity in patience and endowment composition rules out multiplicity throughout the shifted HARA case ($b>0$), for any finite number of types and any $\gamma>1$, through a global coefficient-ratio argument.

Governments increasingly operate centralized, algorithm-run admission clearinghouses that implement affirmative action through reserve systems. To sustain public trust, many such clearinghouses disclose category-specific cutoffs, but cutoffs need not allow participants to verify whether reserved and open seats are correctly assigned. We formulate cutoff-based verifiability as a governance constraint on the clearinghouse: each participant must be able to verify her assigned school and seat type using only her own score and the public cutoffs, under two intuitive verification protocols. In a controlled school choice model with multiple reserve categories, we characterize mechanisms that are individually rational, strategy-proof, and verifiable. The characterization identifies deferred acceptance mechanisms induced by two choice rules. We recommend one rule that assigns reserved seats only when a student cannot secure an open seat on merit, so that every reserved-seat assignment reflects genuine affirmative action. The results explain mechanism choices across China's high school admission systems and provide design guidance for affirmative action systems in Brazil and India.

Informal and privatized transit services, such as minibuses and shared auto-rickshaws, are integral to daily travel in large urban metropolises, providing affordable commutes where formal public transport is inadequate and other options are unaffordable. A defining feature of these systems is their decentralized organization, with drivers providing service in response to rider demand and earning opportunities. While this structure helps fill critical mobility gaps, it can also generate inefficient service patterns when profit-driven driver route choices do not align with system-wide mobility goals. We develop an analytically tractable game-theoretic framework to study incentives underlying informal and privatized transit systems with a fixed menu of routes, quantify efficiency losses from decentralized driver route choice, and design incentive mechanisms to mitigate these inefficiencies. Here, profit-maximizing informal operators (drivers) decide where to provide service and cost-minimizing commuters (riders) decide whether to use these services. Within this framework, we establish tight price of anarchy bounds showing that decentralized, profit-maximizing driver behavior can lead to bounded yet substantial losses in cumulative driver profit and rider demand served and that these losses can be mitigated through targeted interventions: budget-balanced cross-subsidization, which uses route-specific tolls/subsidies to shape driver payoffs, and fare optimization, which changes rider demand and driver margins through centrally regulated route-level fares. Finally, numerical experiments based on a real-world informal transit system in Nalasopara, India, reinforce these findings.

We propose a tractable model of repeated decision problems that combines concern about model misspecification, as in robust control, with a complexity cost, such as Shannon entropy, that makes pessimistic beliefs trade off statistical plausibility against simplicity. In a static setting, stronger complexity aversion selects more concentrated worst-case beliefs and tilts choice toward actions whose adverse scenarios are harder to summarize with a simple narrative. In a dynamic learning environment, complexity aversion can eliminate the endogenous cycles generated by misspecification concerns alone. We use the model to explain scale heterogeneity in discrete choice, probability neglect, and home bias.

This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning extend to the setting with ambiguity: experiments are equivalent to distributions over posterior beliefs, and Blackwell's more informative and more valuable orders coincide. When applied to the setting of robust Bayesian analysis, our results clarify the source of time inconsistency in the Gamma-minimax problem and provide an argument in favor of the conditional Gamma-minimax criterion. We also apply our results to a persuasion game to illustrate that our model provides a natural benchmark for communication under ambiguity.

A welfare-maximizing designer allocates two kinds of goods using two screening instruments: tolls, whose costs are separable from agents' values, and damages, which are more costly to agents whose values for the goods are higher. Tolls include payments, queues, and administrative burdens; damages include quality reductions, delays, and restrictions on use. When agents differ only in their value for one type of good, the designer can never gain from damaging it. However, using damages can be optimal when valuations for both goods are heterogeneous, as the two instruments can ``sort'' agents across the available options in different ways. I provide conditions under which the optimal mechanism includes a damaged option, as well as sufficient conditions under which it does not; in the latter case, the optimal mechanism posts ``market-clearing'' tolls for each good. Intuitively, damages are more likely to be optimal when values for the two goods are positively affiliated, and less likely when high value for one good predicts low value for the other.

We study a screening problem in which an agent privately knows which actions or technologies are feasible and can disclose only a subset to a principal. Once disclosed, feasible options are verifiable and their payoff consequences are publicly known, so private information concerns feasibility rather than payoffs, misreporting restricts the principal's choices directly rather than distorting her beliefs. Assuming feasible sets are ordered by inclusion, we establish a simple characterization of the optimal mechanism, where the principal either behaves as if there is no asymmetric information or locally provides no reward for better proposals. We derive comparative statics and illustrate the framework in applications to managing persuasion, action elicitation, and production-technology elicitation.

We study optimal contracting when workers face career concerns. Labor markets infer ability from performance, but effort affects how informative performance is. This feedback can generate strategic uncertainty: bonuses inducing effort under optimistic beliefs about effort may fail under pessimistic beliefs. We characterize this force through a criterion tied to skill-effort complementarity and solve for the least-cost policy implementing effort in every equilibrium. Under strategic uncertainty, the employer uses dispersed bonuses. High bonuses rule out pessimistic beliefs, raising the reputational stakes and letting lower bonuses motivate effort. Pay dispersion among observationally identical workers grows with career concerns and skill-wage assortativeness.

This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter indexes a planner's attitude towards inequality. This link offers insights into structural properties of matchings and trade-offs between objectives, showing how stability can lead to welfare inequalities, even among similar agents. Our model captures supply-demand imbalances in contexts like spatial markets, school choice, and ride-sharing. We also show that large markets with idiosyncratic preferences can be well approximated by aligned preferences, expanding the applicability of our results.

A preference profile (i.e., a collection of linear preference orders of the voters over a set of alternatives) with $m$ alternatives and $n$ voters is $d$-Manhattan (resp. $d$-Euclidean) if both the alternatives and the voters can be placed into a $d$-dimensional space such that between each pair of alternatives, every voter prefers the one which has a shorter Manhattan (resp. Euclidean) distance to the voter. We study how $d$-Manhattan preference profiles depend on the values $m$ and $n$. First, we provide explicit constructions to show that each preference profile with $m$ alternatives and $n$ voters is $d$-Manhattan whenever $d \ge \min(n, m - 1)$. We further extend this positive result for other $p$-norms with $p \in R_{\ge 1} \cup \{\infty\}$. Second, for $d = 2$, we develop forbidden substructures-preference patterns among small sets of voters that constrain any 2-Manhattan embedding -- and use them to show that the smallest non-2-Manhattan preference profile has either 3 voters and 6 alternatives, or 4 voters and 5 alternatives, or 5 voters and 4 alternatives. This is more complex than the case with $d$-Euclidean preferences (see (Bogomolnaia and Laslier, 2007) and (Bulteau and Chen, 2022)). We also show that $d$-Manhattan preferences imply $(2d-1)$-dimensional single-peakedness, while 2-Manhattanness is incomparable with single-peakedness and single-crossingness.