This study proposes a game theoretic approach toward the analysis of renewable portfolio standard policy (RPS), which is one of the main forces behind promotion of the use of renewable sources for electricity generation. The peculiar attribute of an RPS system, in tracking the compliance of individual profit-maximizer electricity producers with a collective target (share) for renewable sources, resembles a coupled constraint game. After presenting a generic game theoretic model for an RPS system, a special case study will be explored, to pave the path for an analytical outcome. This is accompanied by a result analysis section to investigate the impact of key parameters on the equilibrium, leading to recommendations and future research avenues.