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Theory and Decision
Published in: Theory and Decision 4/2016

24-05-2016

Cournot and Stackelberg equilibrium under strategic delegation: an equivalence result

Author: Giorgos Stamatopoulos

Published in: Theory and Decision | Issue 4/2016

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Abstract

This paper uses the theory of strategic delegation to derive an equivalence between the models of simultaneous and sequential quantity competition in oligopoly. It shows that Cournot and Stackelberg equilibria under managerial delegation are identical provided delegation is sequential under the first framework and simultaneous under the second. Furthermore, the first (second) mover in the game under sequential delegation earns the same profit as the second (first) mover in the game under sequential quantity competition.
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Appendix
Available only for authorised users
Footnotes
1
The issue of contract observability is discussed on pages 17–18.
 
2
The results of the paper do not change if we assume that the objective functions are combinations of profit and revenue (Fershtman and Judd 1987; Sklivas 1987).
 
3
Game H was first studied by Kopel and Loffler (2008) under a linear demand framework.
 
4
An explanation of this equality is given at the end of the example.
 
5
In Lemma A1, we also define what small \(p''(Q)\) means.
 
6
It is interesting to note that Vardy’s result has been challenged by the findings of experimental work (see Huck and Muller 2000).
 
7
The term \((p^G(a))'\) denotes the derivative of the inverse demand function with respect to total quantity Q evaluated at \(Q=Q^G(a)\).
 
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Metadata
Title
Cournot and Stackelberg equilibrium under strategic delegation: an equivalence result
Author
Giorgos Stamatopoulos
Publication date
24-05-2016
Publisher
Springer US
Published in
Theory and Decision / Issue 4/2016
Print ISSN: 0040-5833
Electronic ISSN: 1573-7187
DOI
https://doi.org/10.1007/s11238-016-9548-x

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