interactions among rational players produce outcomes with respect to the preferences of the players. Each player in a game faces a choice among two or more possible strategies. A strategy is a predetermined program of play that tells the i player which action to take in response to every possible strat- egy other players may use . Transportation of natural gas electricity and water allocation for different purposes was studied recently by Ilkihc [2]. He modeled it as static Cournot game on a graph. We study the dynamic game. The dynamic equations are derived. The stability of the equilibrium solution is studied. Prisoner’s dilemma game is used to model the source countries- transit countries- markets interaction on a graph.The problem studied in this letter can be explained by the following example: Assume Russia wants to export gas to two EU countries say EU1, EU2. Assume Azerbaijan wants to export gas to EU2 only. Thus Cournot game exists between Russia and Azerbaijan in EU2. The Russian gas pipelines pass through Belarus hence prisoner’s dilemma game (PD) exists between Russia and Belarus. Simi- larly Azeri gas pipelines pass through Turkey hence PD game exists between Azerbaijan and Turkey. 2