transit countries on the other. In PD game there are two strategies namely to cooperate or to defect. Typically the payoff matrix for such a game is given by The standard dominant strategy is to defect hence both sides lose a lot. A way to solve this problems is through side payments paid by both producers and end users to transit countries. Games on graphs has been studied by May and Sigmund [7]. They have shown that in the case of Prisoner’s dilemma game cooperation can exist easier than the standard game. Dynamical games representing natural gas, electricity and water are studied using Cournot game on a graph. Stability of the unique equilibrium solution is investigated. Prisoner’s dilemma game is used to model the producers- transit countries-end users interactions. The existence of graphs will improve the possibility of cooperation between these countries. 7 4 Conclusions    R S T U   $^{,T > R > U > S}$ (10)