The paper solves investment problems with uncertain factors using game theory.
problem Optimal forward investment in an incomplete market with model uncertainty.
method Combining stochastic differential games and ergodic BSDE approach.
result Representation of robust forward performance processes in factor form.
Paper proves existence and uniqueness of solutions to nonlocal systems, generalizing stochastic game theory.
problem Time inconsistency in stochastic differential games.
method Proves existence and uniqueness of solutions to nonlocal fully-nonlinear parabolic systems.
result Generalizes stochastic game theory to include time-inconsistent preferences.
New method improves convergence for smooth games.
problem Improving convergence for smooth games.
method Stochastic Hamiltonian Gradient Methods (SHGD).
result SHGD converges linearly to the neighbourhood of a stationary point.
Paper solves complex game theory problems with new equations.
problem Zero-sum stochastic games with non-Markovian switching.
method New multidimensional SRE and BSDE solutions.
result Existence and uniqueness of SRE solutions.
The paper extends game theory using Hodge theory on graphs.
problem Generalizing Shapley's value allocation formula for cooperative games on graphs.
method Connecting stochastic path integrals to Hodge-theoretic Poisson's equations on graphs.
result The value allocation operator is the solution to Poisson's equation in combinatorial Hodge theory.
Game theory model shows optimal investment strategy for wealth growth.
problem Minimizing time to reach large wealth in a stochastic asset market.
method Proved strategy of proportional asset investment minimizes expected time.
result Proportional investment strategy asymptotically minimizes time to large wealth.
Improves GANs training through game theory.
problem Hard training of GANs due to antagonistic networks.
method Rewrote GAN training as a variational inequality and introduced a stochastic relaxed forward-backward algorithm.
result Algorithm converges to an exact solution or a neighborhood of it under monotonicity.
Game theory models how agents trade in a risky asset considering price impact and a common signal.
problem Modeling how financial agents liquidate assets in a risky market with price impact and a common signal.
method Formulated and solved a multi-player stochastic differential game and mean field game.
result Equilibrium strategies reveal how agents adjust the predictive trading signal to price impact.
Study improves L∞ estimates and extreme value behavior in stochastic differential games.
problem Analyzing the mean-field limit of diffusive games through master equation.
method Using the Master Equation to approximate state processes and establishing L∞ estimates for the total error. result Established No∞ asymptotic behavior of upper order statistics of Nash states, initiating Extreme Value Theory for stochastic differential games. The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…
Game theory model for optimal trading with end-of-day constraints.
problem Optimal trading strategy in a game between slow and fast traders.
method Coupled stochastic control problems, Fredholm integral equation solution.
result Explicit solution to the game with profitable strategies for both players.
AEC Games model represents software MARL environments better than POSGs.
problem POSGs are conceptually unsuitable for software MARL environments.
method Introduced AEC Games model as an equivalent to POSGs.
result AEC Games model is more representative of software MARL environments.
Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and random disturbances. First, in the single-player case (corresponding to an agent tryi…
The paper analyzes strategic interactions in a multi-agent reinsurance chain using game theory.
problem Strategic behavior and competition among insurers and reinsurers in a multi-layer reinsurance chain.
method Employed Stackelberg differential games and non-zero-sum game models to characterize strategic interactions. Used dynamic programming and game theory to derive equilibrium strategies for investment and reinsurance.
result Intensified competition leads to reduced safety loadings in reinsurance contracts.
Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.
problem Finding Nash equilibrium in mean-field stochastic games with mean-field interaction.
method Proposed a novel approach to derive Nash equilibrium semi-explicitly using operator resolvents and stochastic Fredholm equations.
result Equilibrium of the N-player game converges to mean-field equilibrium, and ε-Nash equilibrium derived as a by-product. Develops a new method for solving generalized eigenvalue problems efficiently.
problem Efficiently solving generalized eigenvalue problems for large datasets.
method Inspired by the Generalized Hebbian Algorithm, develops a game-theory inspired approach to solving GEPs.
result Demonstrates state-of-the-art performance for optimizing Deep CCA.
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent …
Neural networks are known to be vulnerable to adversarial examples. Carefully chosen perturbations to real images, while imperceptible to humans, induce misclassification and threaten the reliability of deep learning systems in the wild. To guard against adversarial examples, we take inspiration from game theory and ca…
Model predicts BESS interactions and price impacts in energy markets.
problem Understanding BESS interactions and price formation in energy markets.
method Stochastic game-theoretic model with linear-quadratic differential game.
result Equilibrium controls and prices derived for BESSs in both heterogeneous and homogeneous settings.
Video games improve vehicle routing performance.
problem Optimizing vehicle routes with unpredictable passenger requests.
method Replaced vehicle routing with a game, trained agents to play.
result General game-playing agents outperform traditional methods.
Study of LQ MFGs in infinite-dimensional Hilbert spaces.
problem Mean field games in infinite-dimensional settings with stochastic dynamics.
method Analysis of coupled semilinear infinite-dimensional stochastic evolution equations, development of Nash equilibrium.
result Characterization of unique Nash equilibrium in the limit of many agents.
The Shapley value theory is used for risk allocation in non-orthogonal risk factors.
problem Risk allocation among non-orthogonal risk factors in financial portfolios.
method Using Shapley value from cooperative game theory to allocate risk contributions.
result Explicit formulas and numerical algorithms for calculating risk allocations are derived.
New framework values football players based on in-game interactions.
problem Valuing football players based on in-game performance.
method Combining financial models and network theory using a passing matrix.
result Dynamic and individualized player valuation framework.
Study optimal reinsurance strategies in a game between insurer and two reinsurers.
problem Optimal reinsurance strategies in a competitive market.
method Stochastic game theory, Stackelberg model, Nash game, time-inconsistent control problem, extended Hamilton-Jacobi-Bellman equation.
result Equilibrium reinsurance strategies and premiums found for exponential claim size.
Neural operators approximate Stackelberg game solutions.
problem Intractability of follower's best-response operator in dynamic Stackelberg games.
method Used attention-based neural operators to approximate the best-response operator.
result Approximate best-response operator yields close game value.
Unified analysis of first-order methods for smooth games using IQCs.
problem Certify convergence rates of first-order methods for smooth and strongly-monotone games.
method Adapted integral quadratic constraints (IQCs) to study first-order methods and derive tight upper bounds of convergence rates.
result First global convergence rate for the negative momentum method with O(κ1.5) iteration complexity. In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric N-player non-zero-sum stochastic differential games, for which we refer as \emph{deep fictitious play}, a multi-stage learning pro…
Deep fictitious play converges to Nash equilibrium in stochastic differential games.
problem Finding Nash equilibrium in large stochastic differential games.
method Decouples the game into sub-optimization problems and solves each player's optimal strategy with deep BSDE method.
result Deep fictitious play converges to the true Nash equilibrium.
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.
In this paper we propose and analyze a class of N-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem. The associated Quasi-Variational-Inequalities include an essential game comp…
Develops asset pricing models with mean field game theory for heterogeneous agents.
problem Tackles equilibrium asset pricing in incomplete markets with heterogeneous agents.
method Uses mean field game theory and mean field backward stochastic differential equations (BSDEs).
result Derives equilibrium risk premium and shows market clearing in the large population limit.
Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.
problem Learning Nash equilibria in zero-sum stochastic games is computationally expensive.
method Entropy-regularized soft policies for Q-function updates.
result Algorithm converges to Nash equilibrium under certain conditions.
The paper analyzes reinsurance strategies in a competitive multi-agent system.
problem Strategic interactions and competitive behavior in multi-layer reinsurance chains.
method Stochastic differential games and non-zero-sum game models to characterize strategic interactions. Dynamic programming and game theory to derive equilibrium strategies.
result Intensified competition reduces safety loadings in reinsurance contracts.
Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a …
Graphon game model simplifies stochastic interactions among agents.
problem Complex interactions among heterogeneous agents in stochastic games.
method Introduced a discrete-time graphon game formulation with a representative player.
result Existence and uniqueness of graphon equilibrium proven with mild assumptions.
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.
It is now well known that decentralised optimisation can be formulated as a potential game, and game-theoretical learning algorithms can be used to find an optimum. One of the most common learning techniques in game theory is fictitious play. However fictitious play is founded on an implicit assumption that opponents' …
This chapter reviews recent advances in multi-agent reinforcement learning.
problem Theoretical foundations for multi-agent reinforcement learning are lacking.
method Selective overview of MARL algorithms with theoretical analysis.
result Identification of new research directions in MARL theory.
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.
Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning method…
Paper studies competitive networks where teams aim to minimize their own objectives, adapting to each other's strategies.
problem Competitive networks where teams have conflicting objectives.
method Proposes diffusion learning algorithms for two classes of network games: zero-sum and non-zero-sum.
result Stability performance of proposed algorithms analyzed and demonstrated through experiments.
Improved KernelSHAP via linear regression for ML model interpretation.
problem Efficiently estimating Shapley values in model-agnostic settings.
method Revisiting KernelSHAP via linear regression, developing techniques for convergence and uncertainty.
result Original KernelSHAP incurs negligible bias for significant variance reduction.
Solves a game between brokers and informed traders using stochastic differential equations.
problem Optimizing wealth in a game between brokers and informed traders with private signals.
method Closed-form solutions to a mean-field game using forward-backward SDEs.
result Optimal trading strategies for both brokers and informed traders are found.
The paper solves TIC LQ control problems using stochastic differential games.
problem Time-inconsistent linear-quadratic stochastic control problems.
method Stochastic differential games, spike variation approach.
result Achieves Nash equilibrium for TIC problems, demonstrating impact of ambiguity aversion.
The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with finite heterogeneous learning rates. In each case, we characterize the macroscopic…
The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.
problem Asset pricing in a market with partial observation and heterogeneous agents.
method Mean field game theory, exponential quadratic Gaussian framework, Kalman-Bucy filtering theory.
result Characterization of equilibrium risk premium through mean field BSDE and construction of unobservable risk premium process.
Paper analyzes algorithms for nonstationary saddle-point optimization problems.
problem Nonstationary saddle-point optimization problems in game theory, reinforcement learning, and machine learning.
method Proposes extragradient and Frank-Wolfe algorithms for online and bandit settings.
result Establishes sub-linear regret bounds for the proposed algorithms.
Developed LQ MFG theory with common noise, proving existence and uniqueness.
problem Linear-quadratic mean field games with common noise.
method Coupled forward-backward stochastic evolution equations (FBSEEs) in Hilbert spaces.
result Existence and uniqueness of solutions for small and arbitrary finite time horizons.