Model analyzes competitive pricing strategies in large markets of perishable products.
problem Maximizing profits in a competitive market of perishable products.
method Mean-field competition model, Hamilton-Jacobi-Bellman equation, iterative numerical algorithm.
result Properties of equilibrium pricing strategies and market dynamics.
Modeling pollution from competing firms using mean-field games.
problem Pollution regulation of competitive firms producing similar goods.
method Developed a mean-field game model with cap-and-trade regulation.
result Explicit solutions found through Riccati differential equations.
Study optimal investment and consumption strategies for competitive agents with habit formation.
problem Optimal investment and consumption strategies for competitive agents with habit formation.
method Formulated n-agent game problems and mean field game problems, derived mean field equilibrium, constructed approximate Nash equilibrium.
result Explicit convergence order of approximate Nash equilibrium can be obtained.
The paper analyzes competition among fund managers using excess logarithmic returns and constructs games to find optimal allocations.
problem Optimal allocation strategies among fund managers considering excess logarithmic returns.
method Constructs both n-player and mean field games to address the competition problem. result The MFE of the MFG represents the limit of n-player game's equilibrium as n approaches infinity. Study N-player and mean-field games in Itô-diffusion markets with competitive or homophilous interactions.
problem Optimal portfolio choice in a common market with N interacting players. method Analyzes N-player and mean-field games in incomplete and complete markets with CARA utilities and random risk tolerances. result Derives explicit or closed-form solutions for equilibrium processes and game values.
Study explores optimal strategies in games with multiple players and mean-field interactions.
problem Optimal strategies in games with multiple players and mean-field interactions.
method Exploration of three different notions of optimality, including mean-field control solution, mean-field coarse correlated equilibria, and mean-field Nash equilibria.
result Approximation of cooperative and competitive equilibria in large N-player games by mean-field control and mean-field equilibria. The paper analyzes optimal investment strategies in a game with jump risk, deriving mean field equilibria.
problem Optimal investment strategies in a game with jump risk and peer competition.
method Formulated mean field game and n-player game models, characterized equilibrium states, and derived approximation errors.
result Explicit mean field equilibrium and approximate Nash equilibrium for large n-player games.
Study optimal investment strategies for competitive agents using Mean Field Games.
problem Optimizing portfolios with relative performance criteria.
method Mean Field Game framework applied to CRRA and CARA utility cases.
result Derivation of optimal investment and consumption strategies.
Study time-inconsistent portfolio optimization for competitive agents with relative performance criteria.
problem Time-inconsistent mean field and n-agent games under relative performance criteria.
method Construct open-loop equilibrium strategies for n-agent games and mean field games.
result Explicit solutions for n-agent games and mean field games, unique in a special class of equilibria.
We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence.
Study Nash equilibrium in mean field portfolio games with random market parameters.
problem Modeling wealth and relative performance in competitive financial markets.
method Martingale optimality principle approach to characterize Nash equilibrium in mean field FBSDE.
result Unique Nash equilibrium found under weak interaction assumption and market parameters independence.
Study many-player investment-consumption games with power FPPs, finding market-risk preference affects consumption.
problem Investment and consumption optimization in a mean field competition setting.
method Solve many-player and mean field games using power FPPs, providing closed-form solutions.
result Market-risk relative consumption preference affects agent's consumption decisions.
We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log-normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mea…
We develop a mean-field theory for multi-component ICA in high dimensions.
problem Understanding multi-component ICA in high-dimensional settings.
method Asymptotically exact mean-field theory for multi-component online ICA.
result Explicit learnability boundaries and competition conditions linking step size, data moments, and initialization.
Study of insurer games with model uncertainty in reinsurance and investment strategies.
problem Model uncertainty and competitive insurers' performance under worst-case scenarios.
method Formulated robust mean-field game for non-linear system, derived closed-form solutions.
result Relative concerns lead to new hedging terms in investment and reinsurance strategies.
Paper studies optimal tracking portfolio in mean field game of large fund competition.
problem Optimal tracking portfolio in large fund competition with relative performance benchmark.
method Formulated mean field game problem, established existence of mean field equilibrium using PDE approach, constructed approximate Nash equilibrium.
result Existence of mean field equilibrium and consistency condition verified.
Efficiently reduces tensor ranks using mean-field approximation.
problem Low-rank approximation of non-negative tensors.
method Mean-field approximation of tensor rank reduction.
result Our algorithm achieves faster and competitive tensor rank reduction.
We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we…
Study on LOB dynamics using mean-field game theory.
problem Modeling liquidity dynamics in limit order books.
method Mean-field stochastic differential equation and control problem formulation.
result Equilibrium density function of LOB can be derived.
We study ranking quantilized mean-field games to select top-performing agents.
problem Selecting top-performing agents in competitive scenarios.
method Developed two formulations: target-based and threshold-based, and provided analytic and semi-explicit solutions.
result Analytic and semi-explicit solutions for quantilized mean-field consistency conditions.
The paper analyzes arbitrage opportunities in a large investor market with common stock noises.
problem Identifying arbitrage opportunities in a market with many competitive investors.
method Stochastic differential games and mean-field systems to study market dynamics and optimal arbitrage.
result Optimal arbitrage is characterized by a solution to a Cauchy PDE involving volatility terms.
MFGs explain and enhance generative models, revealing new model types.
problem Understanding and improving generative models.
method Mean-field games (MFGs) as a framework to explain and enhance generative models.
result Established connections between MFGs and generative flows, diffusions, and gradient flows.
New sampling method uses gradient-free IPS with RKHS velocity field.
problem Efficient sampling from unnormalized target densities.
method Gradient-free interacting particle systems (IPS) with RKHS velocity field.
result IPS produce high-quality samples from various target distributions.
We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and consumption when compared to the averages among the other agents. We derive a closed …
This paper studies how relative performance concerns affect stock prices in a tree-like market model.
problem The impact of relative performance concerns on stock prices in a tree-like market model.
method Mean-field equilibrium analysis in a binomial tree framework with exponential utility.
result Existence and uniqueness of market-clearing mean-field equilibrium in both single- and multi-population settings.
Efficiently reduces rank of non-negative matrices with quadratic time complexity.
problem Efficiently reducing the rank of non-negative matrices.
method Formulated rank reduction as a mean-field approximation using a log-linear model.
result Optimal solution for minimizing KL divergence can be computed in closed form.
Endogenous reinsurance pricing in large insurance markets
problem Endogenous reinsurance pricing in large insurance markets
method Stackelberg leader and insurer equilibrium analysis
result Characterization of insurers' equilibrium retention and Stackelberg equilibria
New framework for portfolio management using binomial markets and game theory.
problem Investment behavior in competitive and incomplete markets.
method Introduces PRFPP framework, constructs and analyzes for both finite and mean field games.
result Relative performance concerns do not always lead to more risky asset investment.
Kernel-based mean-field games use MMD penalties for interaction and target costs.
problem Optimizing mean-field games with specific cost functions.
method Kernel structure, random Fourier U-statistics, neural network training.
result Sample-level convergence theorem and rate of convergence proved.
New model improves deep learning robustness against adversarial attacks.
problem Improving adversarial robustness of deep learning models.
method Local competition principle, LWTA nonlinearities, Bayesian non-parametrics.
result The new model achieves high robustness to adversarial perturbations on MNIST and CIFAR10 datasets.
Investigates portfolio selection among competitive agents with mean-variance preferences.
problem Optimizing portfolios with multi-agent competition and relative wealth comparison.
method Reformulated as a constrained, non-homogeneous stochastic linear-quadratic control problem; derived optimal feedback strategies; used decoupling techniques and fixed-point theory to solve nonlinear BSDEs.
result Characterized three scenarios based on market and competition parameters: unique Nash equilibrium, no Nash equilibrium, or infinitely many Nash equilibria.
This paper studies insurers' robust strategies in a stochastic game with model uncertainty and volatility risk.
problem Model uncertainty and volatility risk in insurers' surplus processes.
method Formulates robust mean-field games with insurers competing based on mean-variance criterion under worst-case scenario.
result Derives semi-closed forms of equilibrium strategies for insurers and mean-field equilibrium, ensuring existence and uniqueness.
A scalable method for accurate inference of low-dimensional parameters in high-dimensional linear regression.
problem Statistical inference for low-dimensional parameters in high-dimensional linear regression models.
method Mean-field variational Bayes approach, focusing on nuisance parameters and conditional distributions.
result Competitive numerical performance and theoretical guarantees for estimation and uncertainty quantification.
DiAL uses Bayesian Dirichlet random fields for active learning with sparse labels.
problem Active learning with limited labeled data.
method Bayesian Dirichlet random field for feature-conditional class probabilities, calibrating with graph Laplacian.
result Competitive performance in low-label rate graph learning tasks.
Bayesian neural networks can be simplified by parameterizing weights as rank-r matrices, reducing parameter count and improving performance.
problem High parameter count in standard Bayesian neural networks.
method Parameterize weights as W=ABop with A∈Rmimesr, B∈Rnimesr, inducing a singular posterior. result PAC-Bayes generalization bounds and loss bounds show improved performance with fewer parameters.
Study optimal treatment assignment policies under strategic agent responses.
problem Learning optimal treatment policies with strategic agents complicates estimation.
method Dynamic model with threshold convergence to mean-field equilibrium, consistent estimator for policy gradient.
result Threshold for treatment assignment converges to mean-field equilibrium threshold under large but finite number of agents.
Energy price forecasting is a relevant yet hard task in the field of multi-step time series forecasting. In this paper we compare a well-known and established method, ARMA with exogenous variables with a relatively new technique Gradient Boosting Regression. The method was tested on data from Global Energy Forecasting …
Market equilibrium price proven in a large-agent model.
problem Proving market equilibrium in a large-agent setting.
method Proved existence of equilibrium price in a complete, continuous time market with infinite agents.
result The equilibrium price dynamics decouple as the number of agents increases.
We analyze a conservative market model for the competition among economic agents in a close society. A minimum dynamics ensures that the poorest agent has a chance to improve its economic welfare. After a transient, the system self-organizes into a critical state where the wealth distribution have a minimum threshold, …
A new method for uncertainty estimation in neural networks using Gaussian-softmax integration.
problem Quantifying uncertainty in neural network predictions.
method Proposes a single-model approach integrating Gaussian distribution with softmax outputs, using mean-field approximation.
result Competitive performance on uncertainty estimation tasks and outperforms many methods on out-of-distribution detection.
Kaggle competitions offer valuable insights for business forecasting.
problem Lack of attention to Kaggle competitions in academic forecasting studies.
method Review of results from six Kaggle competitions featuring real-life business forecasting tasks.
result Global ensemble models outperform local single models in Kaggle competitions.
Paper adds Fisher Information to mean field optimization for faster convergence.
problem Mean field optimization in neural networks training.
method Developed energy-dissipation method and gradient flow on probability space.
result Marginal distributions converge exponentially to minimizer.
Fuses posterior distributions from different datasets using KL divergence.
problem Combining information from multiple datasets with uncertainty.
method Mean field assumption, KL divergence, assign-and-average approach.
result Efficient non-parametric algorithm for fused model computation.
New framework promotes reproducible, domain-agnostic reinforcement learning algorithms.
problem Domain-specific, compute-resource-maximizing, and non-reproducible participant solutions in reinforcement learning competitions.
method Submission retraining, domain randomization, desemantization through domain obfuscation, and compute/environment-sample budget limitation.
result Participant submissions are reproducible, non-specific to the competition environment, and sample/resource efficient.
The study analyzes games and social hierarchies, incorporating luck and depth of competition.
problem Analyzing patterns of wins and losses in games and social hierarchies.
method Generalized probabilistic models incorporating luck and depth of competition.
result Social competition tends to be deeper with many distinct levels, but there is often a chance of upset victories.
Unified q-learning for mean-field jump-diffusion models with unobservable population distribution.
problem Continuous-time q-learning in mean-field jump-diffusion models with unobservable population distribution.
method Proposed decoupled Iq-function for unified policy evaluation in MFG and MFC problems; unified q-learning algorithm based on test policies and averaged martingale orthogonality condition.
result Unified policy evaluation rule for MFG and MFC problems based on decoupled Iq-function.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
New RL algorithms achieve optimal policies with polynomial sample complexity for mean-field problems.
problem Statistical efficiency of Mean-Field Reinforcement Learning with general function approximation.
method Introduce MF-MBED to characterize problem complexity, propose algorithms based on maximal likelihood estimation.
result Rich mean-field RL problems have low MF-MBED, leading to polynomial sample complexity.