Related papers: A Nash-Type Fictitious Game Framework to Time-Inco…
This paper is concerned with an indefinite linear-quadratic mean field games of stochastic large-population system, where the individual diffusion coefficients can depend on both the state and the control of the agents. Moreover, the…
This paper aims to formulate and study the inverse problem of non-cooperative linear quadratic games: Given a profile of control strategies, find cost parameters for which this profile of control strategies is Nash. We formulate the problem…
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 propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large $N$-player stochastic differential games. Following the idea of fictitious play, we recast the $N$-player game into $N$ decoupled…
We present a novel variant of fictitious play dynamics combining classical fictitious play with Q-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games. Our dynamics involves players…
This paper presents a pioneering investigation into discrete-time two-person non-zero-sum linear quadratic (LQ) stochastic games with random coefficients. We derive necessary and sufficient conditions for the existence of open-loop Nash…
This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost…
Non-cooperative dynamic game theory provides a principled approach to modeling sequential decision-making among multiple noncommunicative agents. A key focus has been on finding Nash equilibria in two-agent zero-sum dynamic games under…
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
Decentralised optimisation tasks are important components of multi-agent systems. These tasks can be interpreted as n-player potential games: therefore game-theoretic learning algorithms can be used to solve decentralised optimisation…
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…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
In this paper, we address the inverse problem in the case of linear-quadratic discrete-time dynamic non-cooperative games. Given feedback laws of players that are known to be a Nash equilibrium pair for a discrete-time linear system, we…
$ $This paper addresses the inverse problem for Linear-Quadratic (LQ) nonzero-sum $N$-player differential games, where the goal is to learn parameters of an unknown cost function for the game, called observed, given the demonstrated…
Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…
The notion of fault tolerant Nash equilibria has been introduced as a way of studying the robustness of Nash equilibria. Under this notion, a fixed number of players are allowed to exhibit faulty behavior in which they may deviate…
Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently…