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 N N -player game converges to mean-field equilibrium, and ε \varepsilon ε -Nash equilibrium derived as a by-product. This paper tackles learning Stackelberg equilibrium in asymmetric games efficiently from noisy samples.
problem Learning Stackelberg equilibrium in asymmetric, general-sum games efficiently from noisy samples.
method The paper initiates the theoretical study of sample-efficient learning of the Stackelberg equilibrium in bandit feedback setting.
result Sharp positive results on sample-efficient learning of Stackelberg equilibrium with value optimal up to a fundamental gap identified.
Study equilibrium consumption habits in a large population using mean field games.
problem Equilibrium consumption under external habit formation in a large population.
method Formulated and solved mean field games for linear and multiplicative habit formation preferences, constructed approximate Nash equilibria for large n-player games.
result Characterized mean field equilibrium strategies and derived financial implications.
We introduce CSE for MLSF games and devise online learning algorithms for achieving no-external Stackelberg-regret.
problem Learning equilibrium in leader-follower games with noisy bandit feedback.
method Proposed Correlated Stackelberg Equilibrium (CSE) and online learning algorithms balancing exploration and exploitation.
result Achieves no-external Stackelberg-regret, converging to approximate CSE.
Paper models game theory for defending against data poisoning attacks.
problem Defending against data poisoning attacks using game theory.
method Modeling attacker-defender game, proving non-existence of pure Nash Equilibrium, proposing mixed strategy approach, and developing an algorithm to approximate Nash Equilibrium.
result Demonstrated effectiveness of mixed strategy defense in experiments.
Study Nash equilibrium in non-zero-sum game with Bermudan strategies.
problem Optimizing pay-offs in non-linear non-zero-sum games.
method Recursive construction to find Nash equilibrium.
result Existence of Nash equilibrium in non-zero-sum game.
DREAM learns optimal strategies in imperfect games without needing a simulator.
problem Learning optimal strategies in imperfect-information games with multiple agents.
method DREAM is a deep reinforcement learning algorithm that converges to Nash Equilibria and coarse correlated equilibria.
result DREAM achieves state-of-the-art performance in benchmark games and is competitive with simulator-based algorithms.
Deep neural network solves large multi-agent games for Markovian Nash equilibrium.
problem Finding Markovian Nash equilibrium in large multi-agent stochastic differential games.
method Reformulate as decoupled decision problems, solve iteratively using deep BSDE method.
result Proposed algorithm accurately finds Nash equilibrium in large games.
Two-layer model studies reinsurance contracts and competition between insurer and reinsurers.
problem Modeling and analyzing reinsurance contracts and competition between insurer and reinsurers.
method Two-layer stochastic game model with insurer negotiating with reinsurers, and reinsurers competing for business.
result Existence and uniqueness of equilibrium strategies for the insurer and reinsurers, characterized in semiclosed form.
Study on liquidation games with market drop-out, proving unique equilibria.
problem Analyzing portfolio liquidation with market drop-out constraints.
method Proves existence and uniqueness of equilibria using integral equations.
result Existence and uniqueness of equilibria in both mean-field and finite-player games.
Study of 2 i m e s 2 2 imes 2 2 im es 2 zero-sum games with noisy observations and commitments.
problem Analyzing 2 i m e s 2 2 imes 2 2 im es 2 zero-sum games with noisy observations and commitments. method Modeling a 2 i m e s 2 2 imes 2 2 im es 2 zero-sum game with a leader committing to a strategy and a follower observing a noisy version of the leader's action. result Observing the leader's action is either beneficial or immaterial for the follower, and the equilibrium payoff is bounded.
The paper explores how regularization can lead to convergence in imperfect information games.
problem Finding equilibrium in imperfect information games with imperfect information.
method Investigates Follow the Regularized Leader dynamics and how adding a regularization term can lead to strong convergence guarantees.
result The approach leads to algorithms that converge exactly to the Nash equilibrium in imperfect information games.
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.
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.
GANs may not have Nash equilibria, but proximal training can find solutions.
problem Existence of Nash equilibria in GANs optimization.
method Proximal training approach to find solutions.
result Proximal training finds solutions to GAN problems.
New method finds Nash equilibria faster in multiplayer games.
problem Finding Nash equilibria in multi-player games, especially in noisy environments.
method Extra-gradient with player sampling and variance reduction.
result Proves better convergence rate than full extra-gradient for noisy games.
We study optimal behavior of energy producers under a CO_2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic aspect is captured through a reduced-form price-impact model for the CO_2 allowance…
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.
The paper introduces Robust Correlated Equilibrium for games with time-varying costs and proposes an algorithm to achieve it.
problem Games with time-varying costs and disturbances.
method Proposes Robust Correlated Equilibrium and a decentralized algorithm to learn optimal strategies.
result The algorithm converges to the Robust Correlated Equilibrium, showing no regret for each controller.
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.
Paper solves MFG for partially reversible investment, showing price influence and Nash equilibrium.
problem Solving MFG for partially reversible investment problems.
method Explicit solution for MFG, sensitivity analysis, comparison with single-agent control.
result Solution to MFG is an ε-Nash Equilibrium, ε=O(1/√N).
Policy mirror ascent achieves Nash equilibrium in mean field games without a population generative model.
problem Achieving Nash equilibrium in mean field games without a population generative model.
method Policy mirror ascent, contractive operator, single-path TD learning.
result Policy mirror ascent converges to Nash equilibrium within O ~ ( ε − 2 ) \widetilde{\mathcal{O}}(\varepsilon^{-2}) O ( ε − 2 ) samples. A RL approach finds Nash equilibrium for turn-based zero-sum games.
problem Finding Nash equilibrium in two-player turn-based zero-sum games.
method EIS method combining exploration, policy improvement, and supervised learning.
result EIS method finds an ε-approximate value function of Nash equilibrium in O(ε^(-(d+4))) steps.
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
Entropy regularization improves MFG learning efficiency and stability.
problem Improving Mean Field Game learning efficiency and stability.
method Entropy regularization applied to MFG with learning.
result Entropy regularization yields time-dependent policies and stabilizes convergence.
Policy gradient methods find Nash equilibrium in noisy games.
problem Finding Nash equilibrium in noisy games.
method Policy gradient methods with noise added.
result Policy gradient methods converge to Nash equilibrium in noisy games.
Study efficient offline RL in Markov games with general models.
problem Learn approximate equilibria from offline data in Markov games.
method Use Bellman-consistent pessimism for interval estimation and optimize gap relaxation.
result First framework for sample-efficient offline learning in Markov games, handling all equilibria.
Paper analyzes adversarial attacks and defenses using game theory.
problem Unclear conditions for optimal attacks and defenses in adversarial learning.
method Game-theoretic framework with locally linear decision boundary model.
result Fast Gradient Method attack and Randomized Smoothing defense form a Nash Equilibrium.
Generalizes insider trading model to multiple assets.
problem Modeling informed trading in a multi-asset context.
method Formulated an infinite-dimensional Bayesian trading game.
result Obtained a parsimonious equilibrium with closed-form solutions.
The paper analyzes a game where players must balance short-term and long-term interests, leading to cooperative or competitive outcomes.
problem Analyzing time inconsistency in inter-personal decision-making under non-exponential discounting.
method Iterative procedures and Zorn's lemma to find Nash equilibria between players' intra-personal equilibria.
result Inter-personal equilibria exist and depend on the impatience levels of the players.
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 n n -player and mean field games to address the competition problem. result The MFE of the MFG represents the limit of n n n -player game's equilibrium as n n n approaches infinity. This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model based on spectrally negative Le…
Transformers learn to play games in-context, proving Nash equilibrium.
problem Understanding in-context game-playing capabilities of pre-trained transformers.
method Theoretical guarantees and constructional results for transformer architecture in multi-agent games.
result Pre-trained transformers can learn Nash equilibrium in-context for two-player zero-sum games.
AMM finds optimal contract for LPs to maximize order flow.
problem Maximizing order flow in AMMs with LPs.
method Leader-follower stochastic game, closed-form equilibrium solutions.
result LPs incentivized to add liquidity when external price attracts more noise trading.
Optimal algorithm for two-player zero-sum games with linear parameterization.
problem Finding Nash Equilibrium in two-player zero-sum Markov games with linear transition.
method Nash-UCRL algorithm, Coarse Correlated Equilibrium, Optimism-in-Face-of-Uncertainty.
result Proves i l d e O ( d H T ) ilde{O}(dH\sqrt{T}) i l d e O ( d H T ) regret bound, matching lower bound up to logarithmic factors. This paper improves sample efficiency for learning equilibria in multi-player games.
problem Sample-efficient learning of equilibria in games with many players.
method Designs algorithms for learning CCE and CE with polynomial sample complexity in the number of players.
result First to show polynomial sample complexity for learning CCE and CE in multi-player games.
Deep learning theory for Nash equilibrium in stochastic games.
problem Computing Nash equilibrium in non-zero-sum stochastic differential games.
method Fictitious play applied to deep neural networks for solving N N N -player optimization problems. result Deep learning algorithm converges to open-loop Nash equilibrium under appropriate assumptions.
Proves minimax sample complexity for turn-based stochastic games.
problem Proving theoretical guarantees for reinforcement learning in turn-based stochastic games.
method Developing absorbing TBSG and reward perturbation techniques to handle statistical dependence.
result Empirical Nash equilibrium strategy approximates true Nash equilibrium in turn-based stochastic games.
A game theory study examines gradual concessions in variable contribution games under uncertainty.
problem Gradualism in contribution games due to free rider effect.
method Stochastic game analysis of variable contribution games, extending Nerlove-Arrow model.
result Equilibrium characterized by regular control strategies leading to gradual concession.
This paper analyzes a game between insurer and reinsurer under ambiguity and risk aversion, optimizing reinsurance and investment strategies.
problem Optimizing reinsurance and investment strategies in a game between insurer and reinsurer under ambiguity and risk aversion.
method Stackelberg game, α \alpha α -maxmin mean-variance criterion, Heston's stochastic volatility, Hamilton-Jacobi-Bellman equations, Riccati differential equations. result Excess-of-loss reinsurance is optimal for the insurer, and the equilibrium strategies are determined by specific equations.
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.
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.
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and …
This paper finds an MFE in large stochastic games using reinforcement learning.
problem Finding an equilibrium in large stochastic games is difficult.
method Lower-myopic best response dynamics and posterior sampling for reinforcement learning.
result Policy and action distributions converge to optimal strategies in an MFE.
Paper tackles hidden game problem in AI alignment and language games.
problem Hidden game problem in AI alignment and language games.
method Developed a composition of regret minimization techniques to discover and exploit hidden structures.
result Achieved optimal external and swap regret bounds for rapid convergence to correlated equilibria.
Model explains periodic trading in financial markets through game theory.
problem Understanding periodic trading activities in financial markets.
method Mean-field liquidation game with major-minor players.
result Existence and uniqueness of Nash equilibrium established.
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.