  In this paper, we present a sequential decomposition algorithm equivalent of
Master equation to compute GMFE of GMFG and graphon optimal Markovian policies
(GOMPs) of graphon mean field teams (GMFTs). We consider a large population of
players sequentially making strategic decisions where the actions of each
player affect their neighbors which is captured in a graph, generated by a
known graphon. Each player observes a private state and also a common
information as a graphon mean-field population state which represents the
empirical networked distribution of other players' types. We consider
non-stationary population state dynamics and present a novel backward recursive
algorithm to compute both GMFE and GOMP that depend on both, a player's private
type, and the current (dynamic) population state determined through the
graphon. Each step in computing GMFE consists of solving a fixed-point
equation, while computing GOMP involves solving for an optimization problem. We
provide conditions on model parameters for which there exists such a GMFE.
Using this algorithm, we obtain the GMFE and GOMP for a specific security setup
in cyber physical systems for different graphons that capture the interactions
between the nodes in the system.
