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Global cooperation on climate change mitigation is essential to limit temperature increases while supporting long-term, equitable economic growth and sustainable development. Achieving such cooperation among diverse regions, each with different incentives, in a dynamic environment shaped by complex geopolitical and economic factors, without a central authority, is a profoundly challenging game-theoretic problem. This article introduces RICE-N, a multi-region integrated assessment model that simulates the global climate, economy, and climate negotiations and agreements. RICE-N uses multi-agent reinforcement learning (MARL) to encourage agents to develop strategic behaviors based on the environmental dynamics and the actions of the others. We present two negotiation protocols: (1) Bilateral Negotiation, an exemplary protocol and (2) Basic Club, inspired from Climate Clubs and the carbon border adjustment mechanism (Nordhaus, 2015; Comissions, 2022). We compare their impact against a no-negotiation baseline with various mitigation strategies, showing that both protocols significantly reduce temperature growth at the cost of a minor drop in production while ensuring a more equitable distribution of the emission reduction costs.