dorsal/arxiv
View SchemaCooperation driven by mutations in multi-person Prisoner's Dilemma
| Authors | Anders Eriksson, Kristian Lindgren |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0408021 |
| URL | https://arxiv.org/abs/q-bio/0408021 |
| DOI | 10.1016/j.jtbi.2004.08.020 |
| Journal | Journal of Theoretical Biology, 2005, 232(3), pp. 399 - 409 |
Abstract
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoner's Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that timescale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterised by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterised by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size.
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"abstract": "The n-person Prisoner\u0027s Dilemma is a widely used model for populations where\nindividuals interact in groups. The evolutionary stability of populations has\nbeen analysed in the literature for the case where mutations in the population\nmay be considered as isolated events. For this case, and assuming simple\ntrigger strategies and many iterations per game, we analyse the rate of\nconvergence to the evolutionarily stable populations. We find that for some\nvalues of the payoff parameters of the Prisoner\u0027s Dilemma this rate is so low\nthat the assumption, that mutations in the population are infrequent on that\ntimescale, is unreasonable. Furthermore, the problem is compounded as the group\nsize is increased. In order to address this issue, we derive a deterministic\napproximation of the evolutionary dynamics with explicit, stochastic mutation\nprocesses, valid when the population size is large. We then analyse how the\nevolutionary dynamics depends on the following factors: mutation rate, group\nsize, the value of the payoff parameters, and the structure of the initial\npopulation. In order to carry out the simulations for groups of more than just\na few individuals, we derive an efficient way of calculating the fitness\nvalues. We find that when the mutation rate per individual and generation is\nvery low, the dynamics is characterised by populations which are evolutionarily\nstable. As the mutation rate is increased, other fixed points with a higher\ndegree of cooperation become stable. For some values of the payoff parameters,\nthe system is characterised by (apparently) stable limit cycles dominated by\ncooperative behaviour. The parameter regions corresponding to high degree of\ncooperation grow in size with the mutation rate, and in number with the group\nsize.",
"arxiv_id": "q-bio/0408021",
"authors": [
"Anders Eriksson",
"Kristian Lindgren"
],
"categories": [
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],
"doi": "10.1016/j.jtbi.2004.08.020",
"journal_ref": "Journal of Theoretical Biology, 2005, 232(3), pp. 399 - 409",
"title": "Cooperation driven by mutations in multi-person Prisoner\u0027s Dilemma",
"url": "https://arxiv.org/abs/q-bio/0408021"
},
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