Linear quadratic graphon field games

Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ which involve a large number of agents that weakly coupled via weighted undirected graph on each node represents an agent. The links the correspond couplings between agents' dynamics, as well individual cost functions, agent attempts minimize. We formulate limit LQ-GFG problems based assumption these graphs lie in sequence converges graphon. First, under finite-rank graphon, existence and uniqueness solutions formulated problem is established. Second, upon problem, epsilon-Nash equilibria constructed for corresponding game with very but finite players. This result then generalized case random initial conditions. It noted distinct from class mean (GMFG) where population hypothesized associated [Caines Huang CDC 2018, 2019].