Replicator dynamics for involution in an infinite well-mixed population

Abstract

We propose a new type of group game, the involution game. The group resources are fixed, and individuals compete for the fixed resources by effort. We assume binary strategies: more effort and less effort. More effort means paying more cost to occupy more resources than less effort does. If everyone adopts more effort, they will acquire the same amount of resources as if everyone adopts less effort, but each pays a meaningless extra cost, that is, the involution. We use the method of replicator dynamics in an infinite well-mixed population to investigate the model. The results show that more abundant resources promote involution, and an increase in the relative utility of more effort also aggravates involution. Increasing the cost of more effort may aggravate involution in some parameter ranges, but it ultimately leads to a disincentive to involution. This new type of game may contain considerable potential to explore.