Unifying Cournot and Stackelberg Action in a Dynamic Setting
Heinrich von Stackelberg, like Harold Hotelling, was one of those scientists of the early twentieth Century, who put down many seeds for new original ways to look at old problems in theoretical economics, often pointing at paradoxical issues with no obvious solution. Stackelberg’s contribution to duopoly (von Stackelberg, 1934, 1938), one Century after Cournot’s initiation (Cournot, 1838), is probably his most well known contribution.
Even if Stackelberg departs from Cournot in his leader/follower dichotomy, in contrast to Cournot, there is no clue to any dynamization of the model. It is all static equilibrium theory. One competitor can learn and take account of the Cournot reaction function of the other and then maximize profits. If the latter indeed follows the proper reaction function, everything is fine, there is a Stackelberg equilibrium. The other competitor can do the same, and again, if the first then follows its reaction function, everything is fine again, there is another Stackelberg equilibrium. They can also both adhere to their reaction functions, and then one is back to Cournot’s original case. However, if both competitors attempt leadership at once, then there is trouble; both are disappointed as expectations show up wrong.
What will then happen? Will one of the competitors, or both, resign leadership, and the system go to the Cournot or one of the Stackelberg equilibria? Stackelberg did not give any clue at all to this.
KeywordsPeriodic Orbit Rational Expectation Reaction Function Unit Production Cost Existence Region
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