This paper introduces a new approach to performing a relaxed analysis using a repeated game to achieve an international environmental agreement (IEA) with the full participation of countries when an asymmetric relationship exists with respect to emissions-related benefits and environmental damage. Our model reveals that a stable IEA depends on the magnitude of the relationship between the benefit-cost ratios of the two types of countries, not on their compositions. That is, the number of punishing countries for a weakly renegotiation-proof equilibrium depends on the benefit-cost ratios of the two types of countries. Our results show that a global cooperation on abatement among the two types of countries can be achieved by addressing deviation through flexibly selecting punishing countries based on benefit-cost ratios.
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