The anti-paradox of cooperation: Diversity may pay!

Abstract

This paper considers the stability and success of a public good agreement. We allow for any type and degree of asymmetry regarding benefits and costs. We ask the question whether asymmetry and which type and degree of asymmetry is conducive to cooperation? We employ a simple non-cooperative game-theoretic model of coalition formation and derive analytical solutions for two scenarios: an agreement without and with optimal transfers. A central message of the paper is that asymmetry does not have to be an obstacle for successful cooperation but can be an asset. We qualify two central results in the literature. Firstly, the paradox of cooperation, known since Barrett (1994) and reiterated by many others afterwards, stating that under those conditions when cooperation would matter most, stable agreements achieve only little. Secondly, a kind of “coalition folk theorem”, known (without proof) in the literature for a long time, stating that without transfers, stable coalitions will be smaller with asymmetric than symmetric players. We show that even without transfers the grand coalition can be stable if there is a negative covariance between benefit and cost parameters with massive gains from cooperation. Moreover, with transfers, many distributions of benefit and cost parameters lead to a stable grand coalition, again, some of them implying huge gains from cooperation. Stability and success greatly benefit from a very skewed asymmetric distribution of benefit and costs, i.e., diversity may pay!