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In many real-world dynamical systems, obtaining precise models of system uncertainty remains a challenge. It may be difficult to estimate noise distributions or robustness bounds, especially when the distributions/robustness bounds vary…
This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being…
We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i.e., zero-sum stochastic games). We consider an episodic setting where in each…
Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for…
We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by…
Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient descent ascent (GDA) dynamics in a specific class of non-convex…
High-precision operation of quantum computing systems must be robust to uncertainties and noises in the quantum hardware. In this paper, we show that through a game played between the uncertainties (or noises) and the controls, adversarial…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
We study the last-iterate convergence of variance reduction methods for extragradient (EG) algorithms for a class of variational inequalities satisfying error-bound conditions. Previously, last-iterate linear convergence was only known…
We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…
Recent extensions to dynamic games of the well-known fictitious play learning procedure in static games were proved to globally converge to stationary Nash equilibria in two important classes of dynamic games (zero-sum and…
This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game…
We give a simple proof of the well-known result that the marginal strategies of a coarse correlated equilibrium form a Nash equilibrium in two-player zero-sum games. A corollary of this fact is that no-external-regret learning algorithms…
Concavity and its refinements underpin tractability in multiplayer games, where players independently choose actions to maximize their own payoffs which depend on other players' actions. In concave games, where players' strategy sets are…
Designing efficient algorithms to find Nash equilibrium (NE) refinements in sequential games is of paramount importance in practice. Indeed, it is well known that the NE has several weaknesses, since it may prescribe to play sub-optimal…
In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…
Finding equilibria via gradient play in competitive multi-agent games has been attracting a growing amount of attention in recent years, with emphasis on designing efficient strategies where the agents operate in a decentralized and…
In noncooperative Nash games, equilibria are often inefficient. This is exemplified by the Prisoner's Dilemma and was first provably shown in the 1980s. Since then, understanding the quality of Nash equilibrium (NE) received considerable…
Best-response (BR) schemes represent an important avenue for learning equilibria in noncooperative games. However, extant rate guarantees for BR schemes generally necessitate stringent smoothness requirements on player objectives and the…
We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE seeking algorithm for monotone games that requires one…