An application of differential game theory to a dynamic duopoly problem with maximum production constraints

In this paper an application of differential game theory in the area of microeconomics is presented. The problem considered is that of dynamic duopoly where two firms each limited by a maximum capacity of production, share the same market, and try simultaneously but independently to maximize their profits over a certain planning horizon. Necessary conditions for the Cournot Solution in the general case are discussed and more specific results for the special case of linear demand and quadratic cost functions are developed.