Related papers: Leader-Follower Linear-Quadratic Stochastic Grapho…
This paper considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to…
We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that…
Resource competition problems are often modeled using Colonel Blotto games, where players take simultaneous actions. However, many real-world scenarios involve sequential decision-making rather than simultaneous moves. To model these…
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…
This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and a large number of weakly-coupled interactive followers. The leader and the followers cooperate to optimize the…
This paper addresses a Stackelberg stochastic linear-quadratic (LQ) differential game under closed-loop information, a problem inherently time-inconsistent. Existing approaches rely on solving two coupled Hamilton-Jacobi-Bellman (HJB)…
We consider a distributed stochastic approximation (SA) scheme for computing an equilibrium of a stochastic Nash game. Standard SA schemes employ diminishing steplength sequences that are square summable but not summable. Such requirements…
This paper investigates a robust incentive Stackelberg stochastic differential game problem for a linear-quadratic mean field system, where the model uncertainty appears in the drift term of the leader's state equation. Moreover, both the…
In this paper, the known deterministic linear-quadratic Stackelberg game is revisited, whose open-loop Stackelberg solution actually possesses the nature of time inconsistency. To handle this time inconsistency, {a two-tier game framework…
The $1-N$ generalized Stackelberg game (single-leader multi-follower game) is intricately intertwined with the interaction between a leader and followers (hierarchical interaction) and the interaction among followers (simultaneous…
We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is…
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an $\epsilon$-Nash equilibrium if no player can gain more than $\epsilon$ by…
We provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a…
In this paper, we investigate the noncooperative games of multi-agent systems. Different from existing noncooperative games, our formulation involves the high-order nonlinear dynamics of players, and the communication topologies among…
We study the Stackelberg-Nash null controllability of a coupled system governed by two linear forward stochastic parabolic equations. The system includes one leader control localized in a subset of the domain, two additional leader controls…
This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…
This paper addresses a linear-quadratic Stackelberg mean field (MF) games and teams problem with arbitrary population sizes, where the game among the followers is further categorized into two types: non-cooperative and cooperative, and the…
We investigate the linear quadratic Gaussian Stackelberg game under a class of nested observation information pattern. Two decision makers implement control strategies relying on different information sets: The follower uses its observation…
This paper is concerned with the closed-loop solvability of one kind of linear-quadratic Stackelberg stochastic differential game, where the coefficients are deterministic. The notion of the closed-loop solvability is introduced, which…
Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…