Cooperation in finite populations: Being alone helps. Issue 4 (3rd July 2016)

• Record Type: Journal Article
• Authors: Nguyen, Anh V.; Saini, Jasmeet S.; Rowell, Jonathan T.; Rychtář, Jan
• Is Part Of: Journal of interdisciplinary mathematics. Volume 19:Issue 4(2016)
• Page Start: 799
• Page End: 809
• Publication Date: 2016-07-03
• Subjects: 91A22 -- 92D15; Evolution of Cooperation -- Prisoner's Dilemma -- Hawk-Dove Game -- Evolutionary Dynamics -- Moran Process; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.1080/09720502.2016.1188492
• Languages: English
• ISSNs: 0972-0502

Abstract

Abstract: 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.