Social dilemma; problems in the formation and maintenance of cooperation among selfish individuals, are of fundamental importance for the biological and social sciences. To consider the spontaneous formation of cooperation in society under social dilemma, dynamical systems game is adopted. To be specific, the 'Lumber-jacks' Dilemma (LD) game' is studied, which includes the concrete description of the dynamics of resources depending on players' actions. With the numerical study of the evolution of the strategies in the LD game, it is shown that the cooperation is formed and maintained, through the formation of articulation of strategies based on bifurcation in dynamical systems. Evolution of the cooperative society is found to occur successively with the dynamical change of game structure and of norms adopted in the society. In contrast with the models of the traditional game theory, the cooperation is shown to be sustained even if the number of the members sharing the social dilemma is increased.
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