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…
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48 results for “Stochastic game”
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 -player game converges to mean-field equilibrium, and -Nash equilibrium derived as a by-product.
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.
The paper analyzes a class of stochastic games involving moving free boundaries and Nash equilibria.
problem Analyzing interactions among players in stochastic games with moving free boundaries.
method Deriving sufficient conditions for Nash equilibrium through verification theorems, solving multi-dimensional free boundary problems, and Skorokhod problems.
result An intriguing connection between NE strategies and controlled rank-dependent stochastic differential equations.
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.
Deep Q-Learning method for Nash equilibria in stochastic games.
problem Model-free learning for multi-agent stochastic games, especially for general-sum games.
method Data-efficient Deep-Q-learning using local linear-quadratic expansion parametrized by deep neural networks.
result The algorithm learns optimal actions for stochastic games without experiencing all state-action pairs.
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.
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.
Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximationcs.LG
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.
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.
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.
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.
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.
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.
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.
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.
A Q-learning algorithm finds Nash equilibrium in two-player stochastic games efficiently.
problem Finding Nash equilibrium in two-player stochastic games with limited samples.
method Feature-based Q-learning algorithm with accelerated techniques for improved sample efficiency.
result The algorithm finds an ε-optimal strategy with sample size linear to the number of features and time/space complexity independent of game dimensions.
Algorithmic traders optimize execution and arbitrage in markets with hidden information.
problem Optimal execution and statistical arbitrage in markets with latent factors.
method Solve a large stochastic game with mean-field game limit, using convex analysis and FBSDE.
result Prove the MFG equilibrium is an ε-Nash equilibrium for finite player games.
Omega method mitigates noise in stochastic game optimization.
problem Noise sensitivity and convergence issues in stochastic game optimization.
method Omega method incorporates EMA of historic gradients in its update rule.
result Omega method outperforms optimistic gradient method in stochastic games.
Paper solves discounted stochastic games with near-optimal time and sample complexity.
problem Solving discounted stochastic two-player games with optimal complexity.
method Generalizes Q-learning to two-player strategy computation, overcoming limitations of existing methods.
result Near-optimal -strategy computation with polylogarithmic factors in and .
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 -player optimization problems.
result Deep learning algorithm converges to open-loop Nash equilibrium under appropriate assumptions.
Study examines how traders optimize in a market with differing beliefs about price formation.
problem Optimizing trading actions in a market with heterogeneous beliefs about price formation.
method Analysis of mean-field game limit of a stochastic game with non-standard forward-backward SDEs.
result Nash equilibrium found through a non-standard vector-valued forward-backward SDE, with solutions constructed using expectations of filtered states.
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.
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…
A new algorithm calculates optimal strategies for two-player zero-sum games.
problem Computing the optimal strategies for two-player zero-sum games.
method Extending successive relaxation to two-player zero-sum games and developing a generalized minimax Q-learning algorithm.
result The proposed algorithm converges and effectively computes optimal strategies.
The paper extends macroscopic market making to stochastic games, revealing properties and solving equations.
problem Price competition among market makers in a stochastic game setting.
method Extension of macroscopic market making framework to stochastic games, introducing multidimensional characteristic equations.
result New well-posedness results for forward-backward stochastic differential equations.
New framework compares two stochastic learning dynamics in games.
problem Inability to distinguish between different learning rules leading to the same steady-state behavior.
method Developed a framework for comparative analysis of stochastic learning dynamics with different update rules.
result Identified distinct behaviors in the paths to stochastically stable states for LLL and ML.
Market impact game analyzed with stochastic parameters using FBSDEs.
problem Analyzing Nash equilibrium in a market impact game with stochastic parameters.
method Characterizes Nash equilibrium using fully coupled FBSDEs and provides conditions for their unique solution.
result Unique Nash equilibrium found and characterized in terms of FBSDEs.
Paper presents a GMFG framework for large stochastic games.
problem Learning Nash Equilibrium in large stochastic games.
method Value-based and policy-based reinforcement learning algorithms with smoothed policies.
result Proposed algorithms GMF-V and GMF-P are efficient and robust in GMFG setting.
Nonzero-sum stochastic impulse games with an application in competitive retail energy marketsmath.OC
Study competitive energy markets using stochastic impulse games.
problem Maximizing profits in competitive retail energy markets.
method Connection between Nash equilibrium and quasi-variational inequalities (QVIs).
result Value functions are constrained viscosity solutions of QVIs.
Paper solves complex control problems using novel SDEs.
problem Solving stochastic differential games for nonlinear systems.
method Uses Deep Forward-Backward SDEs with neural networks.
result Numerical solution validated on two example systems.
In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximiza…
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.
The paper tackles multi-agent inverse reinforcement learning in stochastic games, proposing solutions for five variants.
problem Inverse reinforcement learning in multi-agent stochastic games with different solution concepts.
method Developed novel approaches for five variants of multi-agent inverse reinforcement learning (MIRL) in a two-player general-sum stochastic game framework.
result Proposed solutions for five variants of MIRL: uCS-MIRL, advE-MIRL, cooE-MIRL, uCE-MIRL, and uNE-MIRL.
Study improves 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 estimates for the total error.
result Established asymptotic behavior of upper order statistics of Nash states, initiating Extreme Value Theory for stochastic differential games.
Asymptotic minimization of expected time to reach a large wealth level in an asset market gameq-fin.MF
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.
Trading with the Crowdq-fin.TR
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.
SAP prunes activations to defend against adversarial examples.
problem Vulnerability of neural networks to adversarial examples.
method SAP uses a stochastic mixed strategy to prune activations.
result SAP improves accuracy and preserves calibration against adversarial attacks.
Solves game contingent claims using Nash equilibria in incomplete markets.
problem Analyzing game contingent claims in incomplete markets with utility-based hedging.
method Solves the stochastic game corresponding to GCCs with both stopping and trading, constructing Nash equilibria.
result Constructs Nash equilibria for GCCs with utility-based hedging, extending existing literature.
A Mean-Field Game Approach to Equilibrium Pricing in Solar Renewable Energy Certificate Marketsq-fin.MF
Study optimizes SREC generation and trading in solar energy markets.
problem Optimizing solar energy generation and trading in SREC markets.
method Mean-field game approach to solve stochastic game with heterogeneous agents.
result Characterized firms' optimal controls and equilibrium SREC price.
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.
Study on games with degenerate diffusion matrices, proving value existence and convergence.
problem Zero-sum games between singular controller and stopper with degenerate diffusion.
method Probabilistic approach using parameterized approximations, convergence analysis.
result Existence of value and optimal stopping times for the game with degenerate dynamics.
We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solut…
We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a -player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error fo…
Model strategic interactions between market makers and traders to optimize execution.
problem Optimizing execution in markets with strategic interactions.
method Stochastic game modeling with FBSDEs and decoupling approach.
result Established Nash equilibria and global well-posedness for specific models.
In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market …