arXiv research

Study improves $L^{\infty}$ estimates and extreme value behavior in stochastic differential games.

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…

Distributed strategic learning has been getting attention in recent years. As systems become distributed finding Nash equilibria in a distributed fashion is becoming more important for various applications. In this paper, we develop a distributed strategic learning framework for seeking Nash equilibria under stochastic…

A RL approach finds Nash equilibrium for turn-based zero-sum games.

We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions f…

A new algorithm reduces memory and computational needs for reinforcement learning.

Algorithm converges to Nash equilibria in competitive games.

We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entangl…

Study of LQ MFGs in infinite-dimensional Hilbert spaces.

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 tackles stochastic control with mean and higher-order moments, finding Nash equilibria.

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…

Proves minimax sample complexity for turn-based stochastic games.

Optimal algorithm for two-player zero-sum games with linear parameterization.

GANs may not have Nash equilibria, but proximal training can find solutions.

Let $M$ and $N$ be Nash manifolds, and $f$ and $g$ Nash maps from $M$ to $N$. If $M$ and $N$ are compact and if $f$ and $g$ are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, $C^infty$ R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash…

Nash's theorem proved with Günther's trick

Paper optimizes reinforcement learning in self-play games with reduced steps.

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…

Machine learning detects NASH patients from medical claims data.

Develops a game-theoretic approach to solve SGEP efficiently.

Optimal geometric estimates for Kähler manifolds with bounded Nash entropy

DP-NCB algorithm ensures privacy and fairness in bandit decisions.

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 $N$-player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error fo…

The paper examines Nash equilibrium in GANs for stationary Gaussian processes.

New method finds all Nash equilibria via vector optimization.

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 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…

A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems that are expressed in terms of: the consumption plans' optimization problem in pure…

New algorithm finds Nash equilibrium in multi-agent games.

Pessimistic model-based algorithm finds Nash equilibria in zero-sum Markov games from offline data.

Investigates time-inconsistent portfolio selection under MMV preferences.

Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.

We consider a symmetric multi-players zero-sum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by invertible functions. Using the minimax theorem by \cite{sion} we will show that Nas…

The study characterizes Nash maps between semialgebraic sets and their properties.

This paper simplifies complex game dynamics by using a recursive representation.

A method is provided to resolve Lie algebroids with singularities.

A Nash game theory approach allocates capital requirements among financial institutions.

In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substan…

This paper simplifies the Nash Bargaining Solution for use in intellectual property cases.

New RL algorithms find SNE in Markov games with myopic followers.

Two neural network methods solve the master equation for MFGs.

Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.

Paper refines royalty determination using Bayesian methods.

A new method for RLHF using proximal point Nash learning.

An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.

Ancient Ricci flows with bounded Nash entropy have uniform Sobolev inequalities.

We prove that the infinite family of homotopy 4-spheres constructed by Daniel Nash are all diffeomorphic to 4-sphere.