Related papers: Fictitious play in zero-sum stochastic games

A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…

This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…

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…

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…

In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction…

Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its…

We study automated intrusion response and formulate the interaction between an attacker and a defender as an optimal stopping game where attack and defense strategies evolve through reinforcement learning and self-play. The game-theoretic…

We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the…

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 how strategic interaction can arise from controlled quantum dynamics rather than being imposed as an external mathematical structure. We introduce a class of interaction-defined quantum games in which players are represented by…

We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different kinds of controls. We assume that Player 1 uses piecewise-continuous controls, while Player 2 uses impulse…

This paper examines finite zero-sum stochastic games and demonstrates that when the game's duration is sufficiently long, there exists a pair of approximately optimal strategies such that the expected average payoff at any point in the game…

The behaviour of multi-agent learning in many player games has been shown to display complex dynamics outside of restrictive examples such as network zero-sum games. In addition, it has been shown that convergent behaviour is less likely to…

Zero-sum games are a fundamental setting for adversarial training and decision-making in multi-agent learning (MAL). Existing methods often ensure convergence to (approximate) Nash equilibria by introducing a form of regularization. Yet,…

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our…

We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. We characterize the statistics of such systems by their invariant measures which can be shown to be entirely supported on the boundary of the…

We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also…

This paper addresses the challenge of limited observations in non-cooperative multi-agent systems where agents can have partial access to other agents' actions. We present the generalized individual Q-learning dynamics that combine…

We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…

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…