Prediction of special conditions for better management of people is required to achieve major goals of society which is of high value by today’s extensive communications . Mathematics can solve the problem by both game theory and network theory . This study aims at modeling the relationships between people based on particular frequencies of payoff matrix of Prison’s Dilemma and investigating the impact of the network’s symmetry on population’s dynamic of a complex system by considering a constant place for every member . In this model , the game is repeated to make sure of the stable frequency of species . Time series are considered discrete to let all members play the game with their pre-defined neighbors simultaneously , then all members’ payoffs are compared at the same time . Whether each member gets the highest payoff among his/her neighbors or one of his/her neighbors get the highest payoff , he/she considers his/her previous approach or imitates the approach of the neighbor with a higher payoff , respectively for the next round of the game . Three types of regular networks , called square , hexagonal and triangular , are selected for locating species on cells . It was expected to observe a homogenous population faster , the domination of one species over the other one , and a more complex population dynamic by increasing the number of neighbors . The matrix of Prisoner’s Dilemma is simplified for various frequencies , then Defectors and Cooperators competed for 100 times . The following results were obtained for both species in different networks . For square lattice , the approach of cooperation could be seen in most cases and with different population ratios which leads to having the majority of the population . Moreover , coexistence of both species and even domination of the Defector’s approach over the whole population were observed in a duration of payoff by Defectors against Cooperators . For Hexagonal or Honeycomb lattice , cooperation approach will be the winner if the frequency of Defectors is less and the difference between Defectors’ payoff and Cooperators’ one is low . For Triangular lattice , Defector’s approach was the winner because the effect of neighbor’s payoff was significantly low on changing the approach from defection toward cooperation . In addition , the tendency to defect was increasingly high .