论文标题
线性二次Graphon字段游戏
Linear Quadratic Graphon Field Games
论文作者
论文摘要
线性二次Graphon Field Games（LQ-GFGS）被定义为LQ游戏，涉及大量代理，这些代理通过每个节点代表代理的加权无方向的图形弱耦合。图的链接对应于代理动力学之间以及个体成本函数之间的耦合，每个代理都试图最小化。我们基于这些图表为序列的假设来提出极限LQ-GFG问题，该序列将收敛到极限图形。首先，在限制图形上的有限级假设下，建立了解决方案对公式极限LQ-GFG问题的存在和唯一性。其次，基于LQ-GFG问题的解决方案，Epsilon-Nash Equilibria是针对相应的游戏问题构建的，具有很大但有限的玩家。然后将此结果推广到案例，并在随机初始条件下。值得注意的是，LQ-GFG问题与Graphon平均野战游戏（GMFG）的类别不同，其中人群被认为与图[Caines和Huang CDC 2018，2019]的每个节点相关联。
Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ games which involve a large number of agents that are weakly coupled via a weighted undirected graph on which each node represents an agent. The links of the graph correspond to couplings between the agents' dynamics, as well as between the individual cost functions, which each agent attempts to minimize. We formulate limit LQ-GFG problems based on the assumption that these graphs lie in a sequence which converges to a limit graphon. First, under a finite-rank assumption on the limit graphon, the existence and uniqueness of solutions to the formulated limit LQ-GFG problem is established. Second, based upon the solutions to the limit LQ-GFG problem, epsilon-Nash equilibria are constructed for the corresponding game problems with a very large but finite number of players. This result is then generalized to the case with random initial conditions. It is to be noted that LQ-GFG problems are distinct from the class of graphon mean field game (GMFG) problems where a population is hypothesized to be associated with each node of the graph [Caines and Huang CDC 2018, 2019].
