TY - JOUR
T1 - Cooperation can emerge in prisoner's dilemma from a multi-species predator prey replicator dynamic
AU - Paulson, Elisabeth
AU - Griffin, Christopher
N1 - Funding Information:
Portions of Dr. Griffin’s and Ms. Paulson’s work were supported by the Army Research Office under Grant W911NF-13-1-0271. Portions of Dr. Griffin’s work were supported by the National Science Foundation under grant number CMMI-1463482. The authors gratefully acknowledge the feedback from the reviewers and editorial staff.
Publisher Copyright:
© 2016
PY - 2016/8/1
Y1 - 2016/8/1
N2 - In this paper we study a generalized variation of the replicator dynamic that involves several species and sub-species that may interact. We show how this dynamic comes about from a specific finite-population model, but also show that one must take into consideration the dynamic nature of the population sizes (and hence proportions) in order to make the model complete. We provide expressions for these population dynamics to produce a kind of multi-replicator dynamic. We then use this replicator dynamic to show that cooperation can emerge as a stable behavior when two species each play prisoner's dilemma as their intra-species game and a form of zero-sum predator prey game as their inter-species game. General necessary and sufficient conditions for cooperation to emerge as stable are provided for a number of game classes. We also showed an example using Hawk–Dove where both species can converge to stable (asymmetric) mixed strategies.
AB - In this paper we study a generalized variation of the replicator dynamic that involves several species and sub-species that may interact. We show how this dynamic comes about from a specific finite-population model, but also show that one must take into consideration the dynamic nature of the population sizes (and hence proportions) in order to make the model complete. We provide expressions for these population dynamics to produce a kind of multi-replicator dynamic. We then use this replicator dynamic to show that cooperation can emerge as a stable behavior when two species each play prisoner's dilemma as their intra-species game and a form of zero-sum predator prey game as their inter-species game. General necessary and sufficient conditions for cooperation to emerge as stable are provided for a number of game classes. We also showed an example using Hawk–Dove where both species can converge to stable (asymmetric) mixed strategies.
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U2 - 10.1016/j.mbs.2016.05.006
DO - 10.1016/j.mbs.2016.05.006
M3 - Article
C2 - 27318117
AN - SCOPUS:84975879579
SN - 0025-5564
VL - 278
SP - 56
EP - 62
JO - Mathematical Biosciences
JF - Mathematical Biosciences
ER -