arXiv research

New algorithms for RL in Markov games with independent linear function approximation, breaking the curse of multiagents.

New findings show pure strategy equilibria are more robust in a war of attrition game.

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…

Algorithm converges to Nash equilibria in competitive games.

Algorithm minimizes regret and converges to equilibria in Markov games.

Paper optimizes multi-agent learning in Markov games with generative model.

Study optimal stopping times for multi-dimensional processes with non-exponential discounting.

A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …

This paper tackles sample-efficient reinforcement learning for partially observable Markov games.

This work tackles robust RL in multi-agent settings, improving sample efficiency.

New approach tackles non-stationary multi-agent games with black-box methods.

Algorithm finds Nash equilibria in complex games with function approximation.

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

Study efficient offline RL in Markov games with general models.

Method locates equilibria on unknown Riemannian manifolds using iterative sampling and parallel transport.

New MARL algorithms resolve the curse of multiagency with function approximation.

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconve…

There is an increasing demand for computing the relevant structures, equilibria and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension red…

In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…

This paper improves sample efficiency for learning equilibria in multi-player games.

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that me…

Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. We present formulations of inference problems in Markov random f…

Study shows randomized strategies can't be Nash equilibria in markets with transient price impact.

The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.

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…

For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.

Study network equilibria in saturated systems, revealing how small shocks can trigger major losses.

Paper develops efficient algorithms for learning rationalizable equilibria in multiplayer games.

Study global geometry of dynamical systems with entire vector fields.

Imitation learning algorithms can be used to learn a policy from expert demonstrations without access to a reward signal. However, most existing approaches are not applicable in multi-agent settings due to the existence of multiple (Nash) equilibria and non-stationary environments. We propose a new framework for multi-…

V-learning tackles multiagent reinforcement learning by reducing sample complexity.

New results on financial equilibria in markets with general semimartingales.

We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof is also useful in studying the bifurcation of relative equilibria.

This paper analyzes complex equilibria in a networked bivirus epidemic model.

We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.

Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the equilibrium allocation are m…

In this paper the possibility of computing equilibrium in pure exchange and production economies by a homotopy method is investigated. The performance of the algorithm is tested on examples with known equilibria taken from the literature on general equilibrium models and numerical results are presented. In computing eq…

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

We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresh…

The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.

Study of MHD equilibria with orientation-reversing symmetry, showing all orbits are periodic.

Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.

New method finds all Nash equilibria via vector optimization.

We obtain a formula for the number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the winding number of the evolute of $\partial K$ with respect to $O$. The formula extends to the case where $O$ lies on the evolute of $\partial K$ and a suitably modified version ho…

We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here we argue in favor of the usefulness of …

We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.

This work finds mixed equilibria in zero-sum games using interacting particle dynamics.

Given a multifunction from $X$ to the $k-$fold symmetric product $Sym_k(X)$, we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…