# On Dynamical Cournot Game on a Graph 

E.Ahmed $^{∗}$, M.I.Shehata$^{†}$and H.A.El-Saka‡ 

$^{∗†}$Mathematics Department, Faculty of Science, Mansoura 35516, EGYPT 

## 1 Introduction 

Cournot dynamical game is studied on a graph. The stability of the system is studied. Prisoner’s dilemma game is used to model natural gas transmission. 

Key words: Dynamical Cournot game, graph; gas, water and elec- tricity transportation. 

## Abstract 

Game theory [1] was first introduced by von Neumann and Morgenstern in 1944 as a mathematical model. It is the study of ways in which strategic 

