A three-strategy game involving loners in eco-evolutionary dynamics

Recently, eco-evolutionary games (in which there is feedback between strategies and the environment) have been of growing interest and are mostly studied using two strategies-cooperator and defector. In this study, we extend the two strategy eco-evolutionary games to three strategy games by introducing the loner strategy in order to investigate its behaviour in the system and on the environment. We formulated a three-strategy model to establish the replicator dynamics of the coupled evolutionary system and obtained the fixed points to the replicator dynamics. Under different payoff conditions analysed, the system experiences a persistent oscillation when the cooperators and defectors co-exist in the environment with the loners going extinct due to the invasion of defectors. However, when the loners are sustained throughout the environment with the help of the cooperators, no persistent oscillation is observed. On the basis of stability analysis, the phase trajectories show that the cooperators and defectors are stable in the environment while the loners are unstable.