A very challenging subject for scientists is population dynamics, growth and ex- tinction of various species caused by their competition. Game theory is a mathe- matical and logical approach for analysis and simulation of population behavior. In this project, we study competition between two strategies (species) distributed on a square lattice and separated by a circular boundary in the initial state. Each player intracts with it’s nearest neighbors according to the payoff matrix that is defined. Players may imitate the neighbor’s strategy with a probability depending on their payoff difference. Strategy updates can change the structure of species (strategies) in population. Also We analyse the role of noise (which quantifies the frequency of mistake) and edges-rewiring of network in two-strategy evolutionary games and competition of strategies. We checked the relation between the microscopic individual behavior (noise) and the macroscopic properties (edges-rewiring). Our simulation show that change of noise and rewiring can change evolutionary process of strategies. Rewiring changes the boundary between strategies and contact surface. We also found that with increasing rewiring, the effect of noise decrease.
