Revisiting Stackelberg in His Own Light: Conjecture Learning in Leader-Follower Games *

Denis Claude () and Mabel Tidball ()
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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 an 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 under which the learning process converges asymptotically to a self-confirming steadystate. We characterize the resulting activity levels and payoffs in two canonical environments: a sequential partnership game and a sequential duopoly game with quantity competition. We then compare the learning outcomes to both the (complete information) Stackelberg and the cartel solution. In the process, we find conditions under which the lack of information and the resulting strategic ambiguity lead to higher joint payoffs, and under which usual intuitions about the first-mover advantage need qualifications.

Keywords: Leader-follower game; incomplete information; conjectures (search for similar items in EconPapers)
Date: 2026
New Economics Papers: this item is included in nep-mic
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Published in International Game Theory Review, In press

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05571970

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