Stackelberg Duopoly Models Reconsidered

Abstract

In spite of the extensive works done on problems of the Cournot (or Cournot-type) oligopoly models, dynamic analysis of’duopoly model formulated by H.von Stackelberg(1934) has almost been outside the scope of concern of economists. J.M.Henderson and R.E.Quandt(1958) in now a classic on mathematical microeconomics have given an excellent summary of Stackelberg’s fundamental idea on duopoly without, however, giving any systematic analysis of dynamics. As is well known, three cases, that is, follower-follower, leader follower and leader-leader, are considered by Stackelberg. Since any duopolist is in an advantageous position when he becomes a leader, both duopolists strive for leadership. However, “If both desire to be leaders, each assumes that the other’s behavior is governed by his reaction function, but in fact, neither of the reaction function is observed and a Stackelberg disequilibrium is encountered. Stackelberg believed that this disequilibrium is the most frequent outcome. The final result of a Stackelberg disequilibrium cannot be predicted a priori. If Stackelberg was correct, this situation will result in economic warfare, and equilibrium will not be achieved until one has succumbed to the leadership of other or a collusive agreement has been reached”. (Henderson and Quandt(1958, p. 181) )