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The Stackelberg equilibrium as a consistent conjectural equilibrium

Abstract : We consider a static game with conjectural variations where some firms make conjectures while others do not. Two propositions are proved. We first show that there exists a continuum of conjectural variations such that the conjectural equilibrium locally coincides with the Stackelberg equilibrium (Proposition 1). Second, we define the conditions under which a conjectural equilibrium is a locally consistent equilibrium (i.e. such that conjectures are fulfilled). The concept of (local) consistency is restricted to firms making conjectures. Two conditions on consistency are featured: consistency within a cohort and consistency among cohorts. The Stackelberg equilibrium fulfills only the latter condition (Proposition 2). An example is provided.
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Ludovic Julien, Olivier Musy, Aurélien Saidi. The Stackelberg equilibrium as a consistent conjectural equilibrium. Economic Bulletin, Springer Verlag, 2011, 31 (1), pp.938-949. ⟨halshs-01228003⟩

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