CRRA utility and the sustainability of cooperation in infinitely-repeated games

Abstract

In a symmetric infinitely-repeated game, where players have constant relative risk aversion (CRRA), or constant elasticity of intertemporal substitution, utility functions, it is shown that the critical discount factor required to sustain full cooperation is decreasing in the coefficient of relative risk aversion (increasing in the elasticity of intertemporal substitution). An application to cooperation in international environmental agreements (IEA) is presented and it is shown that the limit of the critical discount factor as the number of countries goes to infinity is equal to one (zero) if the coefficient of intertemporal inequality aversion is less (greater) than one. • Analyses infinitely-repeated game when players have CRRA utility functions. • Cooperation in infinitely-repeated games is easier the more risk-averse are players. • Application to International Environmental Agreement with many countries.