"How to keep punishment to maintain cooperation: Introducing social vaccine" (2016) http://dx.doi.org/10.1016/j.physa.2015.08.053 http://dx.doi.org/10.1016/j.p

"How to keep punishment to maintain cooperation: Introducing social vaccine" (2016) http://dx.doi.org/10.1016/j.physa.2015.08.053 http://dx.doi.org/10.1016/j.physa.2015.08.053 ( Under a Creative Commons ) http://www.sciencedirect.com/science/article/pii/S0378437115007189 http://www.sciencedirect.com/science/article/pii/S0378437115... Keywords: Evolutionary game theory; Social dilemma; Free-rider problem; Agent based simulation; Social vaccine Abstract "Although there is much support for the punishment system as a sophisticated approach to resolving social dilemmas, more than a few researchers have also pointed out the limitations of such an approach. Second-order free riding is a serious issue facing the punishment system. Various pioneering works have suggested that an anti-social behavior or noise stemming from a mutation may, surprisingly, be helpful for avoiding second-order freeloaders. In this work, we show through mathematical analysis and an agent-based simulation of a model extending the meta-norms game that the coercive introduction of a small number of non-cooperators can maintain a cooperative regime robustly. This paradoxical idea was inspired by the effect of a vaccine, which is a weakened pathogen injected into a human body to create antibodies and ward off infection by that pathogen. Our expectation is that the coercive introduction of a few defectors, i.e., a social vaccine, will help maintain a highly cooperative regime because it will ensure that the punishment system works."