Mobilia, M (2013) Reply to "comment on 'Stochastic dynamics of the prisoner's dilemma with cooperation facilitators' ". Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 88 (4). 046102. ISSN 1539-3755
Abstract
The fixation properties of a simple prisoner's dilemma game in the presence of "cooperation facilitators" have recently been investigated in finite and well-mixed populations for various dynamics. In a Comment, Miȩkisz claims that, for cooperation to be favored by selection in the standard prisoner's dilemma games with facilitators, it suffices that f C>fD (where fC/D are the respective fitnesses of cooperators and defectors). In this Reply, we show that, in generic prisoner's dilemma games with ℓ cooperation facilitators, it is generally not sufficient that a single cooperator has a higher fitness than defectors to ensure that selection favors cooperation. In fact, it is also necessary that selection promotes the replacement of defection by cooperation in a population of size N, which requires that the fixation probability of a single cooperator exceeds (N-ℓ)-1. This replacement condition is independent of fC>fD and, when the payoff for mutual defection is negative, it is shown to be more stringent than the invasion condition. Our results, illustrated by a series of examples, considerably generalize those reported in the paper and in the aforementioned Comment whose claims are demonstrated to be relevant only for a special subclass of prisoner's dilemma games.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2013, American Physical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Nov 2015 11:35 |
Last Modified: | 23 Jun 2023 21:49 |
Published Version: | http://dx.doi.org/10.1103/PhysRevE.88.046102 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.88.046102 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:87667 |