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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…
We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled…
We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…
We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
In this paper, a Nash-type fictitious game framework is introduced to handle a time-inconsistent linear-quadratic optimal control. The Nash-type game in this framework is called fictitious as it is between the decision maker (called real…
This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of fiinite-player games, the limit of…
We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs…
We study pure Nash equilibria in infinite-duration games on graphs, with partial visibility of actions but communication (based on a graph) among the players. We show that a simple communication mechanism consisting in reporting the…
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…
Fictitious play is an algorithm for computing Nash equilibria of matrix games. Recently, machine learning variants of fictitious play have been successfully applied to complicated real-world games. This paper presents a simple modification…
Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only…
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…
We consider a class of targeted intervention problems in dynamic network and graphon games. First, we study a general dynamic network game in which players interact over a graph and maximize their heterogeneous, concave goal functionals,…
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…
In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
This paper addresses a class of network games played by dynamic agents using their outputs. Unlike most existing related works, the Nash equilibrium in this work is defined by functions of agent outputs instead of full agent states, which…
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…