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Let $T:X\to X $ and $S:Y \to Y$ be continuous maps defined on compact sets. Let $$\varphi_i(\mu,\nu)=\int_{X \times Y} A_i(x,y) d\mu(x) d\nu(y)\;\;{for} \;\; i=1,2,$$ where $\mu$ is $T$-invariant and $\nu$ is $S$-invariant, be pay-off…
We consider dynamic games defined over an infinite horizon, characterized by linear, discrete-time dynamics and quadratic cost functionals. Considering such linear-quadratic (LQ) dynamic games, we focus on their solutions in terms Nash…
This paper investigates the convergence of learning dynamics in Stackelberg games. In the class of games we consider, there is a hierarchical game being played between a leader and a follower with continuous action spaces. We establish a…
The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well known…
Dynamic games provide a fundamental framework for multi-agent decision-making over time, yet computing feedback Nash equilibria (FNEs) in infinite-horizon discrete-time linear-quadratic (LQ) settings remains computationally challenging.…
In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not…
The integration of microgrids that depend on the renewable distributed energy resources with the current power systems is a critical issue in the smart grid. In this paper, we propose a non-cooperative game-theoretic framework to study the…
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…
Graph Neural Networks (GNNs) have led to state-of-the-art performance on a variety of machine learning tasks such as recommendation, node classification and link prediction. Graph neural network models generate node embeddings by merging…
In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action…
Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the actions taken by their neighbors. Extending the framework of…
Information compression techniques are majorly employed to address the concern of reducing communication cost over peer-to-peer links. In this paper, we investigate distributed Nash equilibrium (NE) seeking problems in a class of…
Many real-world datasets have an underlying dynamic graph structure, where entities and their interactions evolve over time. Machine learning models should consider these dynamics in order to harness their full potential in downstream…
We consider dynamic games with linear dynamics and quadratic objective functions. We observe that the unconstrained open-loop Nash equilibrium coincides with a linear quadratic regulator in an augmented space, thus deriving an explicit…
This paper investigates the game theory of resource-allocation situations where the "first come, first serve" heuristic creates inequitable, asymmetric benefits to the players. Specifically, this problem is formulated as a Generalized Nash…
Node classification on static graphs has achieved significant success, but achieving accurate node classification on dynamic graphs where node topology, attributes, and labels change over time has not been well addressed. Existing methods…
We propose locally convergent Nash equilibrium seeking algorithms for $N$-player noncooperative games, which use distributed event-triggered pseudo-gradient estimates. The proposed approach employs sinusoidal perturbations to estimate the…
In this paper, we consider the $n \times n$ two-payer zero-sum repeated game in which one player (player X) employs the popular Hedge (also called multiplicative weights update) learning algorithm while the other player (player Y) adopts…
Existing Graph Neural Networks (GNNs) follow the message-passing mechanism that conducts information interaction among nodes iteratively. While considerable progress has been made, such node interaction paradigms still have the following…
This paper considers the design of fully distributed Nash equilibrium seeking strategies for multi-agent games. To develop fully distributed seeking strategies, two adaptive control laws, including a node-based control law and an edge-based…