title: Spatial evolutionary public goods game on complete graph and dense complex networks.
abstract: We study the spatial evolutionary public goods game (SEPGG) with voluntary or optional participation on a complete graph (CG) and on dense networks. Based on analyses of the SEPGG rate equation on finite CG, we find that SEPGG has two stable states depending on the value of multiplication factor r, illustrating how the "tragedy of the commons" and "an anomalous state without any active participants" occurs in real-life situations. When r is low (<<), the state with only loners is stable, and the state with only defectors is stable when r is high (>>). We also derive the exact scaling relation for r*. All of the results are confirmed by numerical simulation. Furthermore, we find that a cooperator-dominant state emerges when the number of participants or the mean degree, 〈k〉, decreases. We also investigate the scaling dependence of the emergence of cooperation on r and 〈k〉. These results show how "tragedy of the commons" disappears when cooperation between egoistic individuals without any additional socioeconomic punishment increases.
authors: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors: Jinho
authors: J
authors: Kim
authors: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors: Huiseung
authors: H
authors: Chae
authors: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors: Soon-Hyung
authors: SH
authors: Yook
authors: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors: Yup
authors: Y
authors: Kim
mesh_terms: D000533:Altruism; D003299:Cooperative Behavior; D004989:Ethics; D005716:Game Theory; D006801:Humans; D015233:Models, Statistical