Inequality can prevent cooperation in a minimal differential game for climate mitigation

In order to mitigate climate change, cooperation is needed among actors with different levels of power and vulnerability to climate harms. We propose a minimal model for climate mitigation, a two-player continuous-time (differential) game. Each player starts with a fossil fuel stock that determines their contribution to a global emissions pool. Both players suffer damage from climate change due to total cumulative emissions. Each player can pay to reduce their individual fossil stock, which in turn prevents future harm for both players; this is thus a public goods game wherein we label fossil stock reductions as cooperation. We compute the optimal strategies of the players under two forms of inequality: inequality in the players' vulnerability to climate harms, and inequality in their starting fossil fuel stock. Both types of inequality lead to reduced cooperation and greater total emissions, and the least cooperation resulting when both types of inequality are present. We provide simple mechanistic explanations for this result within the context of the model. We also analyse a version of the game where players may invest in renewable energy and find qualitatively similar conclusions.