NFO13018901 ntro Network science14307130355李婧雅 strategy update is totally random. When K >0, there is no uncertainty in the process, which means if the payoff of j is higher than that of i, i will be sure to use j's strategy 3. Theoretical analysis 3.1 prisoners'dilemma in the rule network Nowak and May made researches about the prisoner's dilemma in the two-dimensions quare lattice network. As the picture one shows, in the square lattice network, every node has four neighbor nodes and connected nodes play games with each other. For easier calculation, we set up the temptation of defection T>l, the reward of cooperation R=l, both punishment of defection P and suckers S are 0, so in this situation,it' s called poor prisoners' dilemma(弱囚徒困境) Nowak has proved the evolutionary results of poor prisoners' dilemma and prisoners' dilemma is the same After each time's game, nodes will calculate the payoff of others and itself and choose the strategy that the nodes with the highest payoff used as its new strategy. So it nakes a strategy update. [2 According to Nowak's research, using this strategy update mechanism in the square lattice network, when IsT<2, p doesnt equal to 0 which means it exists the cooperative nodes and these nodes can gather together to form clusters in the network and show the pattern like picture two. In the picture, the dark ones are the cooperative nodes. The clusters consisting of these nodes will have changes in the process of game but will exist in the network all the time. Thats because cooperative ones unite with each other and get the payoff higher than detective ones. Clusters can prevent the invade from defection strategy. [3]INFO130189.01 Intro Network Science 14307130355 李婧雅 6 strategy update is totally random. When K 0 , there is no uncertainty in the process, which means if the payoff of j is higher than that of i, i will be sure to use j’s strategy. 3. Theoretical analysis 3.1 prisoners’ dilemma in the rule network Nowak and May made researches about the prisoner’s dilemma in the two-dimensions square lattice network. As the picture one shows, in the square lattice network, every node has four neighbor nodes and connected nodes play games with each other. For easier calculation, we set up the temptation of defection T>1, the reward of cooperation R=1, both punishment of defection P and suckers S are 0, so in this situation, it’s called poor prisoners’ dilemma(弱囚徒困境). Nowak has proved the evolutionary results of poor prisoners’ dilemma and prisoners’ dilemma is the same. After each time’s game, nodes will calculate the payoff of others and itself and choose the strategy that the nodes with the highest payoff used as its new strategy. So it makes a strategy update.[2] According to Nowak’s research, using this strategy update mechanism in the square lattice network, when 1≤T<2, c doesn’t equal to 0 which means it exists the cooperative nodes and these nodes can gather together to form clusters in the network and show the pattern like picture two. In the picture, the dark ones are the cooperative nodes. The clusters consisting of these nodes will have changes in the process of game but will exist in the network all the time. That’s because cooperative ones unite with each other and get the payoff higher than detective ones’. Clusters can prevent the invade from defection strategy.[3]