Evolutionary Dynamical Behaviors Of Cooperation Phenomena In Public Goods Games

The public goods games widely exist in various complex systems and contain almost all ofour social elements, which formed the foundation of the society. In traditional formulation of thepublic goods games, the defectors are better off and the cooperators in the group tend to zero.However, spontaneous emergence of cooperation in groups is common phenomenon and itsevolution has been a puzzling question receiving extensive attention. In this thesis, the effects ofdensity are investigated coupled with learning and migration. The main contents are as follow:1. We propose a simple spatial public goods game to study the effect of the population density.As the population density is low, the system is driven to enter into a cooperation state because ofnumerous small local groups. As the density increases to a moderate range, the migration of acooperator from a group to become a loner provides another mechanism to promote the evolutionof cooperation. As the density is high enough, the formation of stable domains promotecooperation.2. Compared with the result from a mean field approximation, it is found that the strategylearning and migration take important effects on the mechanisms. An acceleration of migration isbeneficial for defector to capture the cooperator but it is also beneficial for cooperators to formdomains which promoted cooperation through the third mechanism. On the other hand, theincrease of learning range helps the defectors to invade the compact domains of cooperators.3. Combining the dynamic behavior and evolution of cooperation, we introduced he birth-death process in spatial public goods games. It is found that the system would stay in oscillationwhen learning range is large and migration range is small or enter stability in the contrary.