Inertia in spatial public goods games under weak selection

Due to limited cognitive skills for perceptual error or other emotional reasons, players may keep their current strategies even if there is a more promising choice. Such behavior in-ertia has already been studied, but its consequences remained unexplored in the weak selection limit. To fill this gap, we consider a spatial public goods game model where in-ertia is considered during the imitation process. By using the identity-by-descent method, we present analytical forms of the critical synergy factor r*, which determines when co-operation is favored. We find that inertia hinders cooperation, which can be explained by the decelerated coarsening process under weak selection. Interestingly, the critical synergy conditions for different updating protocols, including death-birth and birth-death rules, can be formally linked by the extreme limits of the inertia factor. To explore the robust-ness of our observations, calculations are made for different lattices and group sizes. Monte Carlo simulations also confirm the results.(c) 2023 Elsevier Inc. All rights reserved.