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The evolution of n-player cooperation—threshold games and ESS bifurcations

Bach, Lars LU ; Helvik, T and Christiansen, F B (2006) In Journal of Theoretical Biology 238(2). p.426-434
Abstract
An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an n-player Prisoner's Dilemma game. With reference to biological situations, such as group foraging, we introduce a threshold condition in the number of cooperators required to obtain the collective benefit. In the simplest version, a three-player game, complex behaviour appears as the replicator dynamics exhibits a catastrophic event separating a parameter region allowing for coexistence of cooperators and defectors and a region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond a critical point in cost-benefit space. Moreover, a repelling fixed point of the dynamics acts as a barrier to... (More)
An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an n-player Prisoner's Dilemma game. With reference to biological situations, such as group foraging, we introduce a threshold condition in the number of cooperators required to obtain the collective benefit. In the simplest version, a three-player game, complex behaviour appears as the replicator dynamics exhibits a catastrophic event separating a parameter region allowing for coexistence of cooperators and defectors and a region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond a critical point in cost-benefit space. Moreover, a repelling fixed point of the dynamics acts as a barrier to the introduction of cooperation in defecting populations. The results illustrate the qualitative difference between two-player games and multiple player games and thus the limitations to the generality of conclusions from two-player games. We present a procedure to find the evolutionarily stable strategies in any n-player game with cost and benefit depending on the number of cooperators. This was previously done by Motro [1991. Co-operation and defection: playing the field and the ESS. J. Theor. Biol. 151, 145–154] in the special cases of convex and concave benefit functions and constant cost. (Less)
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author
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type
Contribution to journal
publication status
published
subject
in
Journal of Theoretical Biology
volume
238
issue
2
pages
426 - 434
publisher
Academic Press
external identifiers
  • pmid:16045941
  • wos:000234770700017
  • scopus:29244490111
ISSN
1095-8541
DOI
10.1016/j.jtbi.2005.06.007
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Theoretical ecology (Closed 2011) (011006011)
id
dc41d722-eaf8-4434-8b11-6be8405cea4e (old id 155529)
date added to LUP
2016-04-01 15:44:46
date last changed
2021-09-15 01:03:26
@article{dc41d722-eaf8-4434-8b11-6be8405cea4e,
  abstract     = {An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an n-player Prisoner's Dilemma game. With reference to biological situations, such as group foraging, we introduce a threshold condition in the number of cooperators required to obtain the collective benefit. In the simplest version, a three-player game, complex behaviour appears as the replicator dynamics exhibits a catastrophic event separating a parameter region allowing for coexistence of cooperators and defectors and a region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond a critical point in cost-benefit space. Moreover, a repelling fixed point of the dynamics acts as a barrier to the introduction of cooperation in defecting populations. The results illustrate the qualitative difference between two-player games and multiple player games and thus the limitations to the generality of conclusions from two-player games. We present a procedure to find the evolutionarily stable strategies in any n-player game with cost and benefit depending on the number of cooperators. This was previously done by Motro [1991. Co-operation and defection: playing the field and the ESS. J. Theor. Biol. 151, 145–154] in the special cases of convex and concave benefit functions and constant cost.},
  author       = {Bach, Lars and Helvik, T and Christiansen, F B},
  issn         = {1095-8541},
  language     = {eng},
  number       = {2},
  pages        = {426--434},
  publisher    = {Academic Press},
  series       = {Journal of Theoretical Biology},
  title        = {The evolution of n-player cooperation—threshold games and ESS bifurcations},
  url          = {http://dx.doi.org/10.1016/j.jtbi.2005.06.007},
  doi          = {10.1016/j.jtbi.2005.06.007},
  volume       = {238},
  year         = {2006},
}