Dynamically consistent solution for a pollution management game in collaborative abatement with uncertain future payoffs

Abstract

This paper presents dynamically stable solutions to a class of cooperative differential games of pollution management in collaborative abatement with uncertain future payoffs. Collaborative abatement leads to a decrease in cost due to reduction in duplicated efforts in the process of joint development and brings about an enhancement in the effectiveness of abatement activities via the sharing of knowledge from individual nation's research. It is believed by many researchers to be the key to effective pollution reduction. Uncertainties in future economic performance are prevalent in fast developing countries like China, Brazil and India. This type of uncertainties often hinders the reaching of cooperative agreements in joint pollution control initiatives. In dynamic cooperative games, a credible cooperative agreement has to be dynamically consistent. For dynamic consistency to hold, the agreed upon optimality principle must remain in effect at any instant of time throughout the game along the optimal state trajectory contingent upon the realization of specific random events. In this analysis, dynamically consistent cooperative solutions and analytically tractable payoff distribution procedures contingent upon specific random events are derived. This approach widens the application of cooperative differential game theory to environmental problems where future payoffs are not known with certainty.