content_image/323433.jpg
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 

<img src='content_image/323433.jpg'>

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. 

## 4 Conclusions 

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. 

