Public Goods Game Model With Limited Participation

The puzzle of the altruistic behavior in the multi-agent system is a difficult problem,which is a cross-subject involving multiple disciplines.The public goods game can be regarded as a paradigm to model and explore it.In the traditional definition of the public goods game,the equally Shared interests of all participants lead to the dominant position of defect.Much effort has been made to explain the evolution of cooperation,including the introduction of a risk-averse strategy of voluntary participation,known as the loner strategy.In this paper,we introduce the participation ratio of strategy to discuss the evolution of cooperation in public goods game.Based on repeated public-goods games,this paper considers that the actual number of participants is limited in individuals who choose cooperative strategy and individuals who choose defective strategy in each round of the game.Some compensations will be given to non-participants in each round of the game.Based on this,the corresponding differential equation model is established,and the influence of participation ratio and compensation income on the game process is analyzed by numerical simulation.The results show that the replication dynamics is followed,the compensation value can be adjusted to stabilize the system and then generate cooperation in the stabilized system if the participation proportion is invariant.And under a given compensation value,adjustments can be made on participation proportion to generate cooperation in the stabilized system.The non-participants acted as a catalyst to help people escape from mutual defection into cooperation and induce cooperative behavior.Therefore,compared with the traditional public goods game,the introduction of the participation ratio of strategy can make the stable system to produce cooperation,that is,the participation ratio of limited public goods game is a simple and effective mechanism to promote cooperation.