Finding, counting, or determining the existence of Nash equilibria, where players must play optimally given each others' actions, are known to be computational intractable problems. We ask whether weakening optimality to the requirement that each player merely avoid worst responses -- arguably the weakest meaningful rationality criterion -- yields tractable solution concepts. We show that it does not: any solution concept with this minimal guarantee is ``as intractable'' as pure Nash equilibrium. In general games, determining the existence of no-worst-response action profiles is NP-complete, finding one is NP-hard, and counting them is #P-complete. In potential games, where existence is guaranteed, the search problem is PLS-complete. Computational intractability therefore stems not only from the requirement of optimality, but also from the requirement of a minimal rationality guarantee for each player. Moreover, relaxing the latter requirement gives rise to a tractability trade-off between the strength of individual rationality guarantees and the fraction of players satisfying them.

Micro-structural models of contagion and systemic risk emphasize that shock propagation is inherently multi-channel, spanning counterparty exposures, short-term funding and roll-over risk, securities cross-holdings, and common-asset (fire-sale) spillovers. Empirical implementations, however, often rely on stylized or simulated networks, or focus on a single exposure dimension, reflecting the practical difficulty of reconciling heterogeneous granular collections into a coherent representation with consistent identifiers and consolidation rules. We close part of this gap by constructing an empirically grounded multilayer network for euro area significant banking groups that integrates several supervisory and statistical datasets into layer-consistent exposure matrices defined on a common node set. Each layer corresponds to a distinct transmission channel, long- and short-term credit, securities cross-holdings, short-term secured funding, and overlapping external portfolios, and nodes are enriched with balance-sheet information to support model calibration. We document pronounced cross-layer heterogeneity in connectivity and centrality, and show that an aggregated (flattened) representation can mask economically relevant structure and misidentify the institutions that are systemically important in specific markets. We then illustrate how the resulting network disciplines standard systemic-risk analytics by implementing a centrality-based propagation measure and a micro-structural agent-based framework on real exposures. The approach provides a data-grounded basis for layer-aware systemic-risk assessment and stress testing across multiple dimensions of the banking network.

This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive set of ultra high-frequency equity and foreign exchange tick data recorded at millisecond precision, allowing us to examine the price evolution at the individual order level. We show that in both theory and practice, traditional measures of jump variation based on lower-frequency data tend to spuriously assign a burst of volatility to the jump component. As a result, the true price variation coming from jumps is overstated. Our estimates based on tick data suggest that the jump variation is an order of magnitude smaller than typical estimates found in the existing literature.

A principal delegates choice to an agent whose decision depends on both beliefs and tastes. The principal can steer the delegated decision using two costly instruments: (i) an information policy that determines a Bayes--plausible distribution of posteriors, and (ii) a bias-management policy that shifts the agent's effective taste. We study a binary-state, two-action, convex hull of two benchmark tastes specialization with posterior-separable information costs. The analysis admits an inner--outer decomposition: optimal bias management is bang--bang (either no intervention or the minimal intervention needed to flip the agent's action), while the optimal information policy is characterized by concavification of an endogenous posterior value function that already incorporates optimal management and information costs. This structure clarifies how information acquisition and bias management interact; they can be complements, substitutes, or both depending on the primitives of the model. Information changes which posteriors are realized and hence where management is used; management reshapes the curvature and kinks of the posterior value function and hence the marginal value of information. The model delivers regime classifications for pooling vs. informativeness and for management at different posteriors within informative signals, and highlights how comparative statics can be monotone or non-monotone depending on how concavification contact points move with costs.

We study finite normal-form games in which payoffs are subject to random perturbations and players face uncertainty about how these shocks co-move across actions, an ambiguity that naturally arises when only realized (not counterfactual) payoffs are observed. We introduce the Statistical Equilibrium of Optimistic Beliefs (SE-OB), inspired by discrete choice theory. We model players as \textit{optimistic better responders}: they face ambiguity about the dependence structure (copula) of payoff perturbations across actions and resolve this ambiguity by selecting, from a belief set, the joint distribution that maximizes the expected value of the best perturbed payoff. Given this optimistic belief, players choose actions according to the induced random-utility choice rule. We define SE-OB as a fixed point of this two-step response mapping. SE-OB generalizes the Nash equilibrium and the structural quantal response equilibrium. We establish existence under standard regularity conditions on belief sets. For the economically important class of marginal belief sets, that is, the set of all joint distributions with fixed action-wise marginals, optimistic belief selection reduces to an optimal coupling problem, and SE-OB admits a characterization via Nash equilibrium of a smooth regularized game, yielding tractability and enabling computation. We characterize the relationship between SE-OB and existing equilibrium notions and illustrate its empirical relevance in simulations, where it captures systematic violations of independence of irrelevant alternatives that standard logit-based models fail to explain.

In repeated games, such as auctions, players rely on autonomous learning agents to choose their actions. We study settings in which players have their agents make monetary transfers to other agents during play at their own expense, in order to influence learning dynamics in their favor. Our goal is to understand when players have incentives to use such payments, how payments between agents affect learning outcomes, and what the resulting implications are for welfare and its distribution. We propose a simple game-theoretic model to capture the incentive structure of such scenarios. We find that, quite generally, abstaining from payments is not robust to strategic deviations by users of learning agents: self-interested players benefit from having their agents make payments to other learners. In a broad class of games, such endogenous payments between learning agents lead to higher welfare for all players. In first- and second-price auctions, equilibria of the induced "payment-policy game" lead to highly collusive learning outcomes, with low or vanishing revenue for the auctioneer. These results highlight a fundamental challenge for mechanism design, as well as for regulatory policies, in environments where learning agents may interact in the digital ecosystem beyond a mechanism's boundaries.

Realized ecosystem services (ES) are the actual use of ES by societies, which is more directly linked to human well-being than potential ES. However, there is a lack of a general analysis framework to understand how much ES was realized. In this study, we first proposed a Supply-Demand-Flow-Use (SDFU) framework that integrates the supply, demand, flow, and use of ES and differentiates these concepts into different aspects (e.g., potential vs. actual ES demand, export and import flows of supply, etc.). Then, we applied the framework to three examples of ES that can be found in typical urban green parks (i.e., wild berry supply, pollination, and recreation). We showed how the framework could assess the actual use of ES and identify the supply-limited, demand-limited, and supply-demand-balanced types of realized ES. We also discussed the scaling features, temporal dynamics, and spatial characteristics of realized ES, as well as some critical questions for future studies. Although facing challenges, we believe that the applications of the SDFU framework can provide a systematic way to accurately assess the actual use of ES and better inform management and policy-making for sustainable use of nature's benefits. Therefore, we hope that our study will stimulate more research on realized ES and contribute to a deeper understanding of their roles in enhancing human well-being.

This paper develops a framework to study the statistical power of revealed-preference tests. With randomly sampled budgets and mild smoothness of demand, statistical learning implies that any model consistent with the data must approximate true choice behaviour. We interpret this result as follows: passing a revealed-preference test is informative only to the extent that the data are sufficiently rich to rule out economically meaningful departures from the maintained model. We make this precise by linking sample size and confidence to the magnitude of detectable departures, and by characterising how power rises with additional observations. Extending our approach beyond revealed-preference inequalities to smooth functional restrictions yields practical tests, even when exact revealed-preference tests are computationally infeasible. We also provide confidence intervals for smooth functionals of demand, including welfare effects. Simulations show that standard sample sizes can generate widely different power across models, contextualizing why some conditions ``rarely reject'' in practice.

To completely understand the effects of urban ecosystems, the effects of ecosystem disservices should be considered along with the ecosystem services and require more research attention. In this study, we tried to better understand its formation through the use of cascade flowchart and classification systems and compare their effects with ecosystem services. It is vitally important to differentiate final and intermediate ecosystem disservices for understanding the negative effects of the ecosystem on human well-being. The proposed functional classification of EDS (i.e. provisioning, regulating and cultural EDS) should also help better bridging EDS and ES studies. In addition, we used Beijing as a case study area to value the EDS caused by urban ecosystems and compare the findings with ES values. The results suggested that although EDS caused great financial loss the potential economic gain from ecosystem services still significantly outweigh the loss. Our study only sheds light on valuating the net effects of urban ecosystems. In the future, we believe that EDS valuation should be at least equally considered in ecosystem valuation studies to create more comprehensive and sustainable development policies, land use proposals and management plans.

We study identification in models of aggregate choice generated by unobserved behavioral types. An analyst observes only aggregate choice behavior, while the population distribution of types and their type-level choice patterns are latent. Assuming only minimal and purely qualitative prior knowledge of the process generating type-level choice probabilities, we characterize necessary and sufficient conditions for identifiability. Identification obtains if and only if the data exhibit sufficient cross-type behavioral heterogeneity, which we characterize equivalently through combinatorial matching conditions between types and alternatives, and through algebraic properties of the matrices mapping type-level to aggregate choice behavior.

In a typical school choice application, the students have strict preferences over the schools while the schools have coarse priorities over the students based on their distance and their enrolled siblings. The outcome of a centralized admission mechanism is then usually obtained by the Deferred Acceptance (DA) algorithm with random tie-breaking. Therefore, every possible outcome of this mechanism is a stable solution for the coarse priorities that will arise with certain probability. This implies a probabilistic assignment, where the admission probability for each student-school pair is specified. In this paper, we propose a new efficiency-improving stable `smart lottery' mechanism. We aim to improve the probabilistic assignment ex-ante in a stochastic dominance sense, while ensuring that the improved random matching is still ex-post stable, meaning that it can be decomposed into stable matchings regarding the original coarse priorities. Therefore, this smart lottery mechanism can provide a clear Pareto-improvement in expectation for any cardinal utilities compared to the standard DA with lottery solution, without sacrificing the stability of the final outcome. We show that although the underlying computational problem is NP-hard, we can solve the problem by using advanced optimization techniques such as integer programming with column generation. We conduct computational experiments on generated and real instances. Our results show that the welfare gains by our mechanism are substantially larger than the expected gains by standard methods that realize efficiency improvements after ties have already been broken.

Belief elicitation is ubiquitous in experiments but can distort behavior in the main tasks. We study when, and how, an experimenter can ask for a series of action-dependent belief statistics after a subject chooses an action, while incentivize truthful reports without distorting the subject's optimal action in the main experimental tasks. We first propose a novel mechanism called the Counterfactual Scoring Rule (CSR), which achieves such nondistortionary elicitation of any single belief statistic by decomposing it into supplemental action-independent statistics. In contrast, when eliciting a fixed set of belief statistics without such decomposition, we show that robust nondistortionary elicitation is achievable if and only if the questions satisfy a joint alignment condition with the task payoff. The necessity of joint alignment is established through a graph theoretical approach, while its sufficiency follows from invoking an adaptation of the Becker-DeGroot-Marschak mechanism. Our characterization applies to experiments with general task-payoff structures and belief elicitation questions.

A designer offers vertically-differentiated positions to agents in the absence of transfers. Agents have private outside options and may reject their offers ex-post. The designer has preferences over the quantity of agents who accept each position. We show that under a general condition on the distribution of outside options, an optimal mechanism for the designer offers all agents an identical lottery, and we characterize this mechanism. When our condition does not hold, the optimal mechanism may require screening agents by offering a menu of distinct lotteries. Our results follow from a decomposition of agents' participation probabilities in any feasible mechanism.

This paper rigorously analyzes the properties of the local projection (LP) methodology within a high-dimensional (HD) framework, with a central focus on achieving robust long-horizon inference. We integrate a general dependence structure into h-step ahead forecasting models via a flexible specification of the residual terms. Additionally, we study the corresponding HD covariance matrix estimation, explicitly addressing the complexity arising from the long-horizon setting. Extensive Monte Carlo simulations are conducted to substantiate the derived theoretical findings. In the empirical study, we utilize the proposed HD LP framework to study the impact of business news attention on U.S. industry-level stock volatility.

In this paper, we develop the metric geometry of ranking statistics, proving that the two major permutation distances in the statistics literature -- Kendall tau and Spearman footrule -- extend naturally to incomplete rankings with both coordinate embeddings and graph realizations. This gives us a unifying framework that allows us to connect popular topics in computational social choice: metric preferences (and metric distortion), polarization, and proportionality. As an important application, the metric structure enables efficient identification of blocs of voters and slates of their preferred candidates. Since the definitions work for partial ballots, we can execute the methods not only on synthetic elections, but on a suite of real-world elections. This gives us robust clustering methods that often produce an identical grouping of voters -- even though one family of methods is based on a Condorcet-consistent ranking rule while the other is not.

We introduce a multiscale measure of network instability based on the joint use of Detrended Cross-Correlation Analysis (DCCA) and Minimum Spanning Tree (MST) filtering. The proposed metric, the Elastic Detrended Cross-Correlation Ratio (Elastic DCCR), is defined as a finite-difference measure of the logarithmic sensitivity of the average MST length to the observation scale. It captures how the structure of cross-correlation networks deforms across different investment horizons. When applied to a network of global equity indices, the Elastic DCCR rises sharply during episodes of financial stress, reflecting increased short-term coordination among investors and a contraction of correlation distances. The measure reveals scale-dependent reconfigurations in network topology that are not visible in single-scale analyses, and highlights clear differences between stressed and stable market regimes. The approach does not assume covariance stationarity and relies only on scale-dependent detrended correlations; as a result, it is broadly applicable to other complex systems in which interaction strength varies with scale.

We study instrumental-variable designs where policy reforms strongly shift the distribution of an endogenous variable but only weakly move its mean. We formalize this by introducing distributional relevance: instruments may be purely distributional. Within a triangular model, distributional relevance suffices for nonparametric identification of average structural effects via a control function. We then propose Quantile Least Squares (Q-LS), which aggregates conditional quantiles of X given Z into an optimal mean-square predictor and uses this projection as an instrument in a linear IV estimator. We establish consistency, asymptotic normality, and the validity of standard 2SLS variance formulas, and we discuss regularization across quantiles. Monte Carlo designs show that Q-LS delivers well-centered estimates and near-correct size when mean-based 2SLS suffers from weak instruments. In Health and Retirement Study data, Q-LS exploits Medicare Part D-induced distributional shifts in out-of-pocket risk to sharpen estimates of its effects on depression.

We introduce a Modewise Additive Factor Model (MAFM) for matrix-valued time series that captures row-specific and column-specific latent effects through an additive structure, offering greater flexibility than multiplicative frameworks such as Tucker and CP factor models. In MAFM, each observation decomposes into a row-factor component, a column-factor component, and noise, allowing distinct sources of variation along different modes to be modeled separately. We develop a computationally efficient two-stage estimation procedure: Modewise Inner-product Eigendecomposition (MINE) for initialization, followed by Complement-Projected Alternating Subspace Estimation (COMPAS) for iterative refinement. The key methodological innovation is that orthogonal complement projections completely eliminate cross-modal interference when estimating each loading space. We establish convergence rates for the estimated factor loading matrices under proper conditions. We further derive asymptotic distributions for the loading matrix estimators and develop consistent covariance estimators, yielding a data-driven inference framework that enables confidence interval construction and hypothesis testing. As a technical contribution of independent interest, we establish matrix Bernstein inequalities for quadratic forms of dependent matrix time series. Numerical experiments on synthetic and real data demonstrate the advantages of the proposed method over existing approaches.

We study the instrumental value of conceptual knowledge when making statistical decisions. Such knowledge tells agents how unknown, payoff-relevant states relate. It is distinct from the statistical knowledge gained from observing signals of those states. We formalize this distinction in a tractable framework used by economists and statisticians. Conceptual knowledge is valuable because it empowers agents to design more informative signals. It is more valuable when states are more "reducible": when they can be explained with fewer common concepts. Its value is non-monotone in the number of signals and vanishes when agents have infinitely many signals. Agents who know more concepts can attain the same payoffs with fewer signals. This is especially true when states are highly reducible.

Optimal signaling schemes in information design (Bayesian persuasion) often involve randomization or disconnected partitions of state space, which might be too intricate to be audited or communicated. We propose explainable information design in the context of linear information design with a continuous state space. In the case of single-dimensional state, we restrict the information designer to use $K$-partitional signaling schemes defined by deterministic and monotone partitions of the state space, where a unique signal is sent for all states in each part. We prove that the price of explainability (PoE) -- the ratio between the performances of the optimal explainable signaling scheme and unrestricted signaling scheme -- is exactly $1/2$ in the worst case, meaning that partitional signaling schemes are never worse than arbitrary signaling schemes by a factor of $2$. For a uniform prior, this PoE can be improved to a tight $2/3$. We then extend the analysis to multi-dimensional state spaces by studying two natural explainability notions: convex-partitional policies and axis-aligned rectangular policies. For convex-partitional policies, we prove a tight PoE of $1/(m+1)$, while for rectangular policies we establish a PoE guarantee under uniform prior that is independent of $K$ but unavoidably exponential in $m$. On the computational side, we prove that the exact optimization of explainable policy is NP-hard in general, but provide efficient approximation methods, including an FPTAS for Lipschitz utility functions and a polynomial-time algorithm that achieves the worst-case $1/2$ benchmark for the broad class of discontinuous, piecewise Lipschitz, utility functions.

We study the implications of a central bank digital currency (CBDC) for the transmission of household preference shocks and for welfare in a New Keynesian framework where the CBDC competes with bank deposits for household resources and banks have market power. We show that an increase in the perceived benefit of CBDC has a mildly expansionary effect, weakening bank market power and significantly reducing the deposit spread. As households economize on liquid asset holdings, they reduce both CBDC and deposit balances. However, the degree of bank disintermediation is low, as deposit outflows remain modest. We then examine the welfare implications of CBDC rate setting and find that, compared to a non-interest-bearing CBDC, the gains with standard coefficients for a CBDC interest rate Taylor rule are modest, but they become considerable when the coefficients are optimized. Welfare gains increase with the CBDC benefit, and the optimal policy responses vary with the banking market structure.

A decision-maker faces uncertainty governed by a data-generating process (DGP), which is only known to belong to a set of sequences of independent but possibly non-identical distributions. A robust decision maximizes the expected payoff against the worst possible DGP in this set. This paper characterizes when and how such robust decisions can be \emph{objectively} improved with data -- that is, yield higher expected payoffs under the true DGP regardless of which DGP is the truth. It further develops simple and novel inference procedures that achieve such improvement, while common methods (e.g., maximum likelihood) may fail to do so.

We study how shareholder values shape firms' costly prosocial actions and who bears their costs. We develop a model in which some shareholders are publicly associated with a firm (e.g., founders or other prominent individual blockholders). When the firm takes a visible action under intense media scrutiny, these shareholders can plausibly claim credit and gain reputation, while diversified institutional investors cannot. The key empirical challenge is that influence is rarely observed: many consequential decisions are not subject to shareholder proposals or votes. We therefore use predetermined annual general meeting (AGM) timing combined with large, sudden crises -- COVID-19 and the invasion of Ukraine -- to generate quasi-experimental variation in attention and attribution, and to study highly visible, high-cost actions that were not legally required at onset. Firms with prominent individual blockholders are more likely to donate or exit when their AGM falls at crisis onset, while firms with large diversified institutional owners are less likely to do so. Consistent with our mechanism, online searches rise for prominent individuals after firm actions but not for institutions. Using an intent-to-treat triple-difference design on the 1,000 largest U.S.-listed firms, we find that exposed firms reduce investment, productivity, and profitability by 1--3\% for up to two years, highlighting the shared costs of pursuing the values of a visible minority.

Consider a persuasion game where both the sender and receiver are ambiguity averse with maxmin expected utility (MEU) preferences and the sender can choose an ambiguous information structure. This paper analyzes the game in an ex-ante formulation: the sender first commits to an information structure, and then the receiver best responds by choosing an ex-ante message-contingent action plan. Under this formulation, I show it is never strictly beneficial for the sender to use an ambiguous information structure as opposed to a standard unambiguous one. This result is robust to (i) the players having heterogeneous beliefs over the states, and/or (ii) the receiver having non-MEU, uncertainty-averse preferences. However, it is \emph{not} robust to the sender having non-MEU preferences.