Largest Consistent Set in International Environmental Agreements

Abstract

We study the formation and the stability of International Environmental Agreements (IEAs) in a pollution abatement model with a quadratic cost function. Countries play a two-stage game: in the first stage each country decides to join or not the coalition while, in the second stage, the quantity of pollution abatement is chosen. To analyze the stability of coalition structures in a multiple coalition game, we use the notion of the Largest Consistent Set (LCS) which allows players to be farsighted. Chwe (1994) developed the concept of farsighted stability: an outcome is stable and it is in the LCS if and only if deviations from it or potential further deviations are not unanimously preferred to the original outcome by the coalition considering the deviations. Applying this notion of stability in the IEA context we assume that, when a country or a sub-coalition contemplate exiting or joining an agreement, it takes into account the reactions of other countries ignited by its own actions. The goal of this paper is to identify the resulting stable structures and the LCS, examining the cooperation among countries with respect to an indicator of countries' environmental awareness. We show that large coalitions are possible outcomes of the game if the farsightedness is considered. In particular, we obtain general sufficient conditions that assure the farsighted stability of the Grand Coalition. In a computational way, we prove that if the environmental awareness is larger than a threshold value, the number of coalition structures belonging to LCS goes down with respect to the initial coalition structures and coalitions with singleton countries never exist. Moreover, we present a useful Maple algorithm to compare the cost functions and to determine direct dominance.