Cooperation in finite populations: Being alone helps

We consider the evolution of cooperation in finite populations and we model a scenario where two individuals can interact only if both intend to do so with their counterpart. This feature allows a possibility for individuals to remain alone for a given round and not interact with anybody. Such an in...

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Bibliographic Details
Published inJournal of interdisciplinary mathematics Vol. 19; no. 4; pp. 799 - 809
Main Authors Nguyen, Anh V., Saini, Jasmeet S., Rowell, Jonathan T., Rychtář, Jan
Format Journal Article
LanguageEnglish
Published Taylor & Francis 03.07.2016
Subjects
Evolution of Cooperation
Evolutionary Dynamics
Hawk-Dove Game
Moran Process
Prisoner's Dilemma
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Summary:We consider the evolution of cooperation in finite populations and we model a scenario where two individuals can interact only if both intend to do so with their counterpart. This feature allows a possibility for individuals to remain alone for a given round and not interact with anybody. Such an individual receives a baseline payoff rather than one based upon a matrix game. We provide sufficient conditions on the payoff matrix that will guarantee fixation probabilities to be monotone relative to the baseline payoff. We then apply the findings to the Prisoner's Dilemma and Hawk-Dove games. In both cases, the possibility that an individual might remain alone increases the chances that cooperation or non-aggression fixes within the population. Moreover, weak selection models overlap with our model, and we consider how one can generalize our model even further.
ISSN:0972-0502
2169-012X
DOI:10.1080/09720502.2016.1188492