This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric embeddings.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “Nash dynamics”
Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.
problem Finding mixed Nash equilibria in zero-sum games with multiple players.
method Mean-field gradient descent dynamics with time-averaging, incorporating exponentially discounted gradients.
result Exponential convergence rate to mixed Nash equilibrium with respect to total variation metric.
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.
Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not typically met in practice. Mixed Nash equilibria exist in greater generality and may be …
New algorithm for solving minimax problems over distributions converges to Nash equilibrium.
problem Solving minimax problems over probability distributions.
method Symmetric Mean-field Langevin Dynamics (MFL-AG and MFL-ABR) with weighted averaging and best response dynamics.
result Converges to mixed Nash equilibrium with average-iterate and last-iterate convergence.
A new method for RLHF using proximal point Nash learning.
problem Capturing real human preferences in RLHF.
method Proximal point Nash learning, embedding self-play updates into a proximal point framework.
result High-probability last-iterate convergence for the combined method.
Study Nash equilibria in mean field portfolio games with consumption.
problem Finding Nash equilibria in mean field portfolio games with consumption.
method Established a correspondence between equilibria and solutions to FBSDEs, using martingale and dynamic programming principles.
result Proved the uniqueness of Nash equilibrium in closed form under certain conditions.
Policy Gradient Methods Find the Nash Equilibrium in N-player General-sum Linear-quadratic Gamesmath.OC
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.
Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.
problem Finding mixed Nash equilibria in continuous games.
method Two-scale Mean-Field Gradient Descent Ascent dynamics.
result Two-scale Mean-Field GDA converges exponentially to MNE without convexity assumptions.
Smooth calibration improves forecast reliability even with leaked information.
problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.
Dynamic pricing policy converges to Nash equilibrium with low regret.
problem Sequential price competition among sellers over multiple periods.
method Semi-parametric least-squares estimation of s-concave demand functions.
result Prices converge to Nash equilibrium with rate and sellers incur regret .
Modeling dealer competition, internalisation and externalisation impact market dynamics and costs.
problem Understanding and optimizing dealer competition in risky asset markets.
method Variational approach to derive Nash equilibrium for dealer competition.
result Dealers using internalisation are incentivized to increase externalisation, leading to higher hedging costs and wider spreads.
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…
Mutation improves FTRL convergence in zero-sum games.
problem Lack of last-iterate convergence in FTRL variants.
method Introduced mutation to perturb action probabilities in FTRL.
result M-FTRL converges to Nash equilibria under full-information feedback.
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.
We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical systems theory. For both general-sum and potential games, we characterize a non…
NAMEx merges experts using Nash bargaining for improved performance.
problem Sparse Mixture of Experts merging strategies lack a principled weighting mechanism.
method Reinterpreting expert merging through game theory, introducing Nash Merging and complex momentum.
result NAMEx consistently outperforms competing methods across various tasks and system sizes.
Evolution of the distribution of wealth in an economic environment driven by local Nash equilibriaq-fin.GN
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general assumptions on the cost function. This evolution drives the dynamic of the agents i…
Investors' strategic trading affects asset prices, modeled as a game.
problem Investors' trading rates influence asset prices in dynamic markets.
method Model as a non-zero sum singular stochastic differential game, establishing equivalence between best-response and auxiliary control problems.
result Unique Nash equilibrium is deterministic with a closed-form solution.
We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost functions, while the aggregated effect of the agents is captured by the population mean o…
A new algorithm reduces memory and computational needs for reinforcement learning.
problem Memory and computational inefficiency in model-free reinforcement learning.
method Memory-Efficient Nash Q-Learning (ME-Nash-QL) for two-player zero-sum games.
result Proves ME-Nash-QL reduces space and sample complexity for tabular and long-horizon cases.
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 analyzes how multiple investors can exploit relative arbitrage opportunities.
problem Analyzing how multiple investors can exploit relative arbitrage opportunities.
method Constructing a well-posed market dynamical system of McKean-Vlasov type, deriving optimal strategies, and finding Nash equilibrium.
result The conditions for relative arbitrage opportunities among competitive investors are derived.
Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.
problem Learning dynamics in bilinear saddle-point problems with bandit feedback.
method Uncoupled learning algorithm combining experimental design and FTRL with a tailored regularizer.
result Last-iterate convergence rate of in high probability.
Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.
problem Learning dynamics in zero-sum polymatrix games under different information settings.
method Two-timescale learning dynamics combining smoothed best-response updates and TD-learning for estimating local payoff functions.
result Polynomial-time finite-sample guarantees for convergence to an ε-Nash equilibrium in the minimal information case.
Learning Two-Player Mixture Markov Games: Kernel Function Approximation and Correlated Equilibriumcs.LG
Algorithm finds Nash equilibria in complex games with function approximation.
problem Learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation.
method Online learning algorithm using upper and lower confidence bounds derived from optimism in the face of uncertainty.
result Achieves regret with polynomial complexity, under mild assumptions.
By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [], inflation [] and nominal interest rate [$…
Two firms compete in a financial market, choosing dividend strategies to avoid default and maximize profits.
problem Strategic interaction between two financially constrained firms in a market with default risk.
method Construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control.
result Explicit identification of optimal strategies and equilibrium payoffs for different initial conditions.
A game-theoretic analysis of DEX competition through dynamic trading fees.
problem Competition between decentralized exchanges (DEXs) and their impact on trading fees and slippage.
method Characterization of an approximate Nash equilibrium via coupled system of partial differential equations and closed-form expressions for equilibrium fees.
result The equilibrium trading fees shift from the oracle price to a weighted average of the oracle and competitors' exchange rates under competition.
Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.
problem Time-inconsistent stochastic control problems with mean and higher-order moments.
method Developed closed-loop and open-loop Nash equilibrium controls using PDEs and maximum principles.
result Identical closed-loop and open-loop Nash equilibria controls, independent of state value and random path.
Let and be Nash manifolds, and and Nash maps from to . If and are compact and if and are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash…
We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum linear quadratic games, a classic game setting which is recently emerging as a b…
Study analyzes portfolio liquidation games influenced by self-exciting order flow.
problem Analyzing portfolio liquidation strategies with market order dynamics.
method Mean-field control problem, novel FBSDE system, sufficient maximum principle.
result Existence and uniqueness of open-loop Nash equilibria proved.
Nash's theorem proved with Günther's trick
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
Investor and firm optimize sustainable investment and emission reduction through a dynamic game.
problem Optimal sustainable investment and emission reduction in a dynamic game setting.
method Formulated as a nonzero-sum dynamic game, solved via variational inequalities and verified in a diffusive setup.
result Nash equilibria show moving boundaries increasing with emission abatement, triggered by both investor and firm actions.
Expands MFGs to handle real-world asymmetric multi-agent games efficiently.
problem Applying mean-field games to real-world, heterogeneous multi-agent systems.
method Develops a method to symmetrize and extend finite-player games to infinite-player MFGs, proving approximation bounds and convergence guarantees.
result TD learning converges to approximate Nash equilibria in finite-sample settings, enabling symmetrized learning without explicit MFG models.
NOHD optimizes multi-agent systems by decomposing dynamics into irrotational and solenoidal components.
problem Non-stationarity and conflicting interests in multi-agent learning problems.
method NOHD (Newton Optimization on Helmholtz Decomposition) decomposes system dynamics into irrotational and solenoidal components.
result NOHD ensures quadratic convergence in purely irrotational and solenoidal systems and attracts to stable fixed points in general multi-agent systems.
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…
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.
Machine learning detects NASH patients from medical claims data.
problem Detecting undiagnosed NASH patients for screening and management.
method Gradient-boosted decision trees trained on administrative medical claims data.
result Model precision for NASH detection is significantly higher than NASH incidence.
Develops forecast hedging for improved calibration of forecasts.
problem Improving the accuracy of forecasted frequencies.
method Combines deterministic and stochastic approaches to forecast hedging.
result Ensures expected track record can only improve.
Optimal geometric estimates for Kähler manifolds with bounded Nash entropy
problem Optimal geometric estimates for compact Kähler manifolds
method Proving Sobolev-type inequality and local volume noncollapsing with optimal exponents
result Uniformly bounded -Nash entropy
This paper simplifies complex game dynamics by using a recursive representation.
problem Difficulties in finite-player dynamic games with private information.
method Provides a recursive representation and noise-state model.
result Equilibrium becomes a deterministic fixed point in impulse-response functions.
Paper analyzes strategic underreporting in competitive insurance markets.
problem Strategic underreporting by insureds in competitive insurance markets.
method Develops a dynamic insurance market model with two competing companies and a continuum of insureds, examines the interaction between strategic underreporting and competitive pricing under a Bonus-Malus System framework.
result Establishes the existence and uniqueness of the insureds' optimal reporting barrier and its dependence on BMS premiums; proves the existence of Nash equilibrium premium strategies.
The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
problem Existence and uniqueness of Nash equilibrium in GANs for stationary Gaussian processes.
method Analyzes the existence of Nash equilibrium in GANs for stationary Gaussian processes, considering different discriminator families.
result The existence of Nash equilibrium depends on the discriminator family and symmetry properties of the generator family.
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nas…
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configu…