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Noncooperative oligopoly equilibrium in markets with hierarchical competition

Ludovic Julien

No 2021-14, EconomiX Working Papers from University of Paris Nanterre, EconomiX

Abstract: This paper deals with the existence of a non-cooperative sequential equilibrium in interrelated markets with heterogeneous atomic traders. Since this model features a rich set of strategic interactions, there are two kinds of problems associated with the existence of equilibrium. First, existence and uniqueness of followers' strategies are not guaranteed. Second, the no-trade equilibrium is always an equilibrium outcome. To overcome these two difficulties we consider a differentiable approach. We show that the set of equations which determines the strategies of followers is a variety with the required dimension, i.e. the vector mapping which defines this set is a local C²-diffeomorphism. The continuous differentiability of followers' strategies is critical for the existence of an interior equilibrium. Unlike the simultaneous move games, exchange can take place in one subgame while autarky can hold in another subgame, in which case only leaders (followers) make trade. Some examples buttress the approach and discuss the assumptions made on the primitives.

Keywords: Pure strategies; diffeomorphisms; Stackelberg-Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C72 D52 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2021
New Economics Papers: this item is included in nep-cwa and nep-gth
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