Emergence and resilience of cooperation in the spatial prisoner's dilemma via a reward mechanism

9 pages, 5 figures.-- ArXiv pre-print available at: http://arxiv.org/abs/0706.0648Final publisher version available Open Access at: http://gisc.uc3m.es/~cuesta/papers-year.htmlWe study the problem of the emergence of cooperation in the spatial Prisoner's Dilemma. The pioneering work by Nowak and May [1992. Evolutionary games and spatial chaos. Nature 415, 424–426] showed that large initial populations of cooperators can survive and sustain cooperation in a square lattice with imitate-the-best evolutionary dynamics. We revisit this problem in a cost–benefit formulation suitable for a number of biological applications. We show that if a fixed-amount reward is established for cooperators to share, a single cooperator can invade a population of defectors and form structures that are resilient to re-invasion even if the reward mechanism is turned off. We discuss analytically the case of the invasion by a single cooperator and present agent-based simulations for small initial fractions of cooperators. Large cooperation levels, in the sustainability range, are found. In the conclusions we discuss possible applications of this model as well as its connections with other mechanisms proposed to promote the emergence of cooperation.This work is partially supported by Ministerio de Educación y Ciencia (Spain) under Grants Ingenio-MATHEMATICA, MOSAICO and NAN2004-9087-C03-03 and by Comunidad de Madrid (Spain) under Grants SIMUMAT and MOSSNOHO.Publicad