The evolution of n-player cooperation—threshold games and ESS bifurcations
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/155529
- author
- Bach, Lars LU ; Helvik, T and Christiansen, F B
- organization
- publishing date
- 2006
- 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
- 2022-01-28 06:49:31
@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}},
}