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In this paper, we investigate the prison's dilemma game with monte carlo rulein the view of the idea of the classic Monte Carlo method on the grid.  Monte carlo rule is an organic combination of the current dynamic rules ofindividual policy adjustment, which not only makes full use of information butalso reflects the individual's bounded rational behavior and the ambivalencebetween the pursuit of high returns and high risks. In addition, it alsoreflects the individual's behavioral execution preferences.  The implementation of monte carlo rule brings an extremely good result,higher cooperation level and stronger robustness are achieved by comparing withthe unconditional imitation rule, replicator dynamics rule and fermi rule.  When analyse the equilibrium density of cooperators as a function of thetemptation to defect, it appears a smooth transition between the mixed state ofcoexistence of cooperators and defectors and the pure state of defectors whenenhancing the temptation, which can be perfectly characterized by thetrigonometric behavior instead of the power-law behavior discovered in thepioneer's work.  When discuss the relationship between the temptation to defect and theaverage returns of cooperators and defectors, it is found that cooperators'average returns is almost a constant throughout the whole temptation parameterranges while defectors' decreases as the growth of temptation.  Additionally, the insensitivity of cooperation level to the initial densityof cooperators and the sensitivity to the social population have been bothdemonstrated.

Cooperation on the monte carlo rule Prison's dilemma game on the grid