Formation of international environmental agreements and payoff allocation

Dealing with climate change requires that all countries engage in costly efforts to reduce their emissions. Reaching this objective has so far been elusive because it is in the best interest of each country to let the others do the effort and benefit itself from a better environment. The presence of negative externalities and strategic behavior have made game theory a natural paradigm to design an international environmental agreement (IEA) that codifies what countries should do. Considering that countries are sovereign and no supranational entity can impose an agreement, a stream of literature adopted a noncooperative mode of play to the formation of an environmental coalition. On the other hand, as joint optimization of all countries’ payoff leads to the best outcome, cooperative games approach has also been proposed to share the cost of climate change. Both approaches have their pros and cons. In this paper, we propose a model of coalition formation that combines both cooperative and noncooperative modes of play. Starting from any given coalition, we implement a Markov process that shows sequentially which countries join or leave the coalition until reaching an absorbing state. All possible sequential scenarios are considered and an allocation to the player is made taking into account individual rationality. An illustration with vulnerable and invulnerable countries to pollution is given