Evolutionary dynamics of a 3-strategy game: Cooperator, defector and costly cooperative loner strategic types

Limiting the analysis to the so-called prisoner's dilemma situation, a new framework of 3-strategy game is proposed herein by adding a costly cooperative loner (CL) to the original strategies; cooperator and defector. Relaying on the replicator dynamics that presumes an infinite and well-mixed population, a set of equilibria is deliberately drawn. In contrast to the expectations from this study, the introduction of CL did not substantially alter the evolutionary trails and always ended with all-defectors state. Some arguments on why such counter-intuitive result comes about is are discussed. The outcomes are justified by the CL's dependency on the other two strategic types and the reduced power in foiling defectors compared to the paradigmatic costly punisher model.