Governance of risky public goods under graduated punishment

Ensuring global cooperation often poses governance problems shadowed by the tragedy of the commons, as wrong-doers enjoy the benefits set up by right-doers at no cost. Institutional punishment of wrongdoers is well-known to curtail their impetus as free-riders. However, institutions often have limited scope in imposing sanctions, more so when these are strict and potentially viewed as disproportionate. Inspired by the design principles proposed by the late Nobel Prize Elinor Ostrom, here we study the evolution and impact of a new form of institutional sanctioning, where punishment is graduated, growing with the incidence of free-riding. We develop an analytical model capable of identifying the conditions under which this design principle is conducive to the self-organization of stable institutions and cooperation. We employ evolutionary game theory in finite populations and non-linear public goods dilemmas in the presence of risk of global losses whose solution requires the self-organization of decision makers into an overall cooperative state. We show that graduated punishment is more effective in promoting widespread cooperation than conventional forms of punishment studied to date, being also less severe and thus, presumably, easier to implement. This effect is enhanced whenever the costs of its implementation are positively correlated with the severity of punishment. We frame our model within the context of the global reduction of carbon emissions, but the results are shown to be general enough to be applicable to other collective action problems, shedding further light into the origins of Human institutions.This research was supported by FCT-Portugal through grants PTDC/EEI-SII/5081/2014, PTDC/MAT/STA/3358/2014, UID/BIA/04050/2013 and UIDB/50021/2020