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Cooperation on the Monte Carlo rule: prisoner’s dilemma game on the grid. (English) Zbl 1457.91049

Sun, Xiaoming (ed.) et al., Theoretical computer science. 37th national conference, NCTCS 2019, Lanzhou, China, August 2–4, 2019. Revised selected papers. Singapore: Springer. Commun. Comput. Inf. Sci. 1069, 3-15 (2019).
Summary: In this paper, we investigate the prisoner’s dilemma game with Monte Carlo rule in the view of the idea of the classic Monte Carlo method on the grid. The Monte Carlo rule is an organic combination of the current dynamic rules of individual policy adjustment, which not only makes full use of information but also reflects individual’s bounded rational behavior and the ambivalence between the pursuit of high returns and high risks. In addition, it also reflects individual’s behavioral execution preferences. The implementation of Monte Carlo rule brings an extremely good result, higher cooperation level and stronger robustness are both achieved by comparing with unconditional imitation rule, replicator dynamics rule and Fermi rule. When analyse the equilibrium density of cooperators as a function of the temptation to defect, it appears a smooth transition between the mixed state of coexistence of cooperators and defectors and the pure state of defectors when enhancing the temptation, which can be perfectly characterized by the trigonometric behavior instead of the power-law behavior discovered in the pioneer’s work. When discuss the relationship between the temptation to defect and the average returns of cooperators and defectors, it is found that cooperators’ average returns is almost a constant throughout the whole temptation parameter ranges while defectors’ decreases as the growth of temptation. Additionally, the insensitivity of cooperation level to the initial density of cooperators and the sensitivity to the social population have been both demonstrated.
For the entire collection see [Zbl 1423.68038].

MSC:

91A12 Cooperative games
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References:

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