A differential game model for a developing and a developed country

A differential game (DG) model for a developing and a developed country is considered. Each player makes decisions about how much resource to be used to restrict the opponent's development so as to maximize his weighted sum of current consumption and final output. Current consumption is assumed to be preferred to final output for both players. The developing country is assumed to have a higher economic growth rate and a higher preference to final output, whereas the developed country is assumed to have a higher initial income and a higher efficiency in restricting his opponent. This problem is investigated under three kinds of information structures, i.e., a zerosum, a nonzero-sum, and a Stackelberg game. Open-loop equilibrium solutions are obtained for all the three cases. Economic implications of the result are provided. The research is supported by the National Natural Science Foundation of China under Grant Nos. 70771118 and 70371030 and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry under Grant No. 2006.331.