Cost of Institutional Incentives for Promoting Cooperation in $$2\times 2$$ Games and Collective Risk Games

Abstract Prosocial behaviours have been extensively studied across multiple disciplines. Cooperation, requiring a personal cost for collective benefits, is widespread in nature and human society, having been explained through mechanisms such as kin selection, direct and indirect reciprocity, and network reciprocity. Institutional incentives, which reward cooperation and punish anti-social behaviour, offer a promising approach to promoting cooperation in groups of self-interested individuals. Focusing on general $$2\times 2$$ games and the collective risk game (a fundamental model for climate action), we analyse the associated cost of providing incentives under evolutionary dynamics governed by Fermi’s rule. Moreover, we explore the asymptotic behaviour of the incentive cost functions in the limits of neutral drift and strong selection. We also implement numerical simulations to study how parameters such as the intensity of selection affect the behaviour of the aforementioned cost functions.