Randomness and diversity matter in the maintenance of the public resources

Most previous models about the public goods game usually assume two possible strategies, i.e., investing all or nothing. The real-life situation is rarely all or nothing. In this paper, we consider that multiple strategies are adopted in a well-mixed population, and each strategy represents an investment to produce the public goods. Past efforts have found that randomness matters in the evolution of fairness in the ultimatum game. In the framework involving no other mechanisms, we study how diversity and randomness influence the average investment of the population defined by the mean value of all individuals' strategies. The level of diversity is increased by increasing the strategy number, and the level of randomness is increased by increasing the mutation probability, or decreasing the population size or the selection intensity. We find that a higher level of diversity and a higher level of randomness lead to larger average investment and favor more the evolution of cooperation. Under weak selection, the average investment changes very little with the strategy number, the population size, and the mutation probability. Under strong selection, the average investment changes very little with the strategy number and the population size, but changes a lot with the mutation probability. Under intermediate selection, the average investment increases significantly with the strategy number and the mutation probability, and decreases significantly with the population size. These findings are meaningful to study how to maintain the public resource.

[1]  Long Wang,et al.  Interaction stochasticity supports cooperation in spatial Prisoner's dilemma. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Attila Szolnoki,et al.  Punish, but not too hard: how costly punishment spreads in the spatial public goods game , 2010, 1007.0431.

[3]  Matjaz Perc,et al.  Does strong heterogeneity promote cooperation by group interactions? , 2011, ArXiv.

[4]  Attila Szolnoki,et al.  Evolutionary dynamics of group interactions on structured populations: a review , 2013, Journal of The Royal Society Interface.

[5]  Daniele Vilone,et al.  Disentangling social and group heterogeneities: Public Goods games on complex networks , 2011, ArXiv.

[6]  Long Wang,et al.  One step memory of group reputation is optimal to promote cooperation in public goods games , 2013 .

[7]  C. Hauert,et al.  Punishing and abstaining for public goods , 2006, Proceedings of the National Academy of Sciences.

[8]  C. Hauert,et al.  Reward and punishment , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[9]  G. Szabó,et al.  Competition of individual and institutional punishments in spatial public goods games. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Long Wang,et al.  Cooperation induced by random sequential exclusion , 2016 .

[11]  David G. Rand,et al.  Evolution of fairness in the one-shot anonymous Ultimatum Game , 2013, Proceedings of the National Academy of Sciences.

[12]  György Szabó,et al.  Phase transitions and volunteering in spatial public goods games. , 2002, Physical review letters.

[13]  Attila Szolnoki,et al.  Competition and cooperation among different punishing strategies in the spatial public goods game , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Matjaz Perc,et al.  Success-Driven Distribution of Public Goods Promotes Cooperation but Preserves Defection , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  M. Perc,et al.  Group-Size Effects on the Evolution of Cooperation in the Spatial Public Goods Game , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Long Wang,et al.  Interactive diversity promotes the evolution of cooperation in structured populations , 2016 .

[17]  Attila Szolnoki,et al.  Reward and cooperation in the spatial public goods game , 2010, ArXiv.

[18]  C. Hauert,et al.  Punishment and reputation in spatial public goods games , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[19]  Long Wang,et al.  Social exclusion in finite populations. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Long Wang,et al.  Evolutionary dynamics of general group interactions in structured populations. , 2016, Physical review. E.

[21]  Long Wang,et al.  Cooperation induced by wise incentive allocation in spontaneous institution , 2016 .

[22]  Attila Szolnoki,et al.  Topology-independent impact of noise on cooperation in spatial public goods games. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.