Revisiting Stackelberg in his own light

Denis Claude () and Mabel Tidball ()
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Denis Claude: LEDi - Laboratoire d'Economie de Dijon [Dijon] - UBE - Université Bourgogne Europe
Mabel Tidball: CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier

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Abstract: This paper revisits Heinrich F. von Stackelberg's original description of leader-follower games under incomplete information, exploring how learning dynamics shape strategic interaction. The leader iteratively updates its conjecture about the follower's reaction function before choosing the activity level that maximizes its payoff. The follower, in turn, responds optimally to each activity level, revealing information that the leader uses to refine its conjecture. Assuming linear conjectures, a smooth updating process à la Jean- Marie and Tidball (2006), and quadratic payoff functions, we establish conditions for which the learning process converges asymptotically. We characterize the outcomes of the learning process in terms of activity levels and payoffs, within both a sequential partnership game and a sequential duopoly game with quantity competition. Moreover, we compare these outcomes to those of the complete information solution and the cooperative solution. In the process, we uncover conditions under which the lack of information, and resulting strategic ambiguity, leads to higher joint payoffs, and under which usual intuitions about the first mover advantage need qualifications.

Keywords: Leader-follower game Incomplete information Conjectures Learning; Leader-follower game; Incomplete information; Conjectures; Learning (search for similar items in EconPapers)
Date: 2025-03-13
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