相关论文: Bridging Finite and Infinite-Horizon Nash Equilibr…

For a class of finite horizon first order mean field games and associated N-player games, we give a simple proof of convergence of symmetric N-player Nash equilibria in distributed open-loop strategies to solutions of the mean field game in…

Iterative linear-quadratic (ILQ) methods are widely used in the nonlinear optimal control community. Recent work has applied similar methodology in the setting of multiplayer general-sum differential games. Here, ILQ methods are capable of…

A growing number of machine learning architectures, such as Generative Adversarial Networks, rely on the design of games which implement a desired functionality via a Nash equilibrium. In practice these games have an implicit complexity…

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

Linear Dynamic Logic on finite traces LDLf is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in…

Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…

In this paper, we study the necessary and sufficient conditions for ensuring the well-posedness of the stochastic singular systems. Moreover, we investigate the stochastic singular linear-quadratic control problems, considering both finite…

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…

The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash…

We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…

We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…

The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We…

We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and…

A Nash equilibrium has become important solution concept for analyzing the decision making in Game theory. In this paper, we consider the problem of computing Nash equilibria of a subclass of generic finite normal form games. We define…

We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it. The scheme is implemented with a single spin qubit system and two entangled qubit system. The Nash Equilibrium…

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…

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE…

We study linear-quadratic stochastic differential games on directed chains inspired by the directed chain stochastic differential equations introduced by Detering, Fouque, and Ichiba. We solve explicitly for Nash equilibria with a finite…

In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of…