Related papers: Empirical Centroid Fictitious Play: An Approach Fo…
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…
We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an…
The paper studies fictitious play (FP) learning dynamics in continuous time. It is shown that in almost every potential game, and for almost every initial condition, the rate of convergence of FP is exponential. In particular, the paper…
We introduce a simple extensive-form algorithm for finding equilibria of two-player, zero-sum games. The algorithm is realization equivalent to a generalized form of Fictitious Play. We compare its performance to that of a similar…
As the earliest and one of the most fundamental learning dynamics for computing NE, fictitious play (FP) has being receiving incessant research attention and finding games where FP would converge (games with FPP) is one central question in…
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…
While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…
In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to…
A multi-agent system operates in an uncertain environment about which agents have different and time varying beliefs that, as time progresses, converge to a common belief. A global utility function that depends on the realized state of the…
Fictitious play (FP) is a history-based strategy to choose actions in normal-form games, where players best-respond to the empirical frequency of their opponents' past actions. While it is well-established that FP converges to the set of…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
A game theoretic distributed decision making approach is presented for the problem of control effort allocation in a robotic team based on a novel variant of fictitious play. The proposed learning process allows the robots to accomplish…
Fictitious Play (FP) is a simple and natural dynamic for repeated play with many applications in game theory and multi-agent reinforcement learning. It was introduced by Brown (1949,1951) and its convergence properties for two-player…
This paper addresses the distributed Nash Equilibrium seeking problem for aggregative games, where legitimate players' decisions are affected by potential malicious players. To describe players' behavior, we introduce a novel heterogeneous…
We consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player's objective is a function of the aggregate of all the players' decisions. Every player maintains an…
Multi-team games, prevalent in robotics and resource management, involve team members striving for a joint best response against other teams. Team-Nash equilibrium (TNE) predicts the outcomes of such coordinated interactions. However, can…
Potential games and decentralised partially observable MDPs (Dec-POMDPs) are two commonly used models of multi-agent interaction, for static optimisation and sequential decisionmaking settings, respectively. In this paper we introduce…
We propose a distributed algorithm for multiagent systems that aim to optimize a common objective when agents differ in their estimates of the objective-relevant state of the environment. Each agent keeps an estimate of the environment and…
Multiple autonomous agents interact over a random communication network to maximize their individual utility functions which depend on the actions of other agents. We consider decentralized best-response with inertia type algorithms in…
Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…