Linear Quadratic Graphon Field Games

Understand

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.