期刊
PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
卷 276, 期 1660, 页码 1379-1384出版社
ROYAL SOC
DOI: 10.1098/rspb.2008.1546
关键词
one-third law; finite populations; cooperation; evolutionary stability; fixation probability; public goods game
资金
- Japan Ministry of Education, Culture, Sports, Science and Technology [18770217]
- Grants-in-Aid for Scientific Research [18770217] Funding Source: KAKEN
Evolution of cooperation has been a major issue in evolutionary biology. Cooperation is observed not only in dyadic interactions, but also in social interactions involving more than two individuals. It has been argued that direct reciprocity cannot explain the emergence of cooperation in large groups because the basin of attraction for the 'cooperative' equilibrium state shrinks rapidly as the group size increases. However, this argument is based on the analysis of models that consider the deterministic process. More recently, stochastic models of two-player games have been developed and the conditions for natural selection to favour the emergence of cooperation in finite populations have been specified. These conditions have been given as a mathematically simple expression, which is called the one-third law. In this paper, we investigate a stochastic model of n-player games and show that natural selection can favour a reciprocator replacing a population of defectors in the n-player repeated Prisoner's Dilemma game. We also derive a generalized version of the one-third law (the {2/[n(n+1)]}(1/(n-1)) law). Additionally, contrary to previous studies, the model suggests that the evolution of cooperation in public goods game can be facilitated by larger group size under certain conditions.
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