Master equation of discrete time graphon mean field games and teams

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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.