Endogenous timing in a mixed duopoly
type: Item
instance of: scholarly article
title: Endogenous timing in a mixed duopoly
zbMATH Open document ID: 1305.91180
author: Rabah Amir
author: Giuseppe De Feo
published in: International Journal of Game Theory
publication date: 2014-08-29T00:00:00Z
full work available at URL: https://strathprints.strath.ac.uk/7230/
review text: Two firms, a private profit maximizing one and a public social welfare maximizing one, compete in quantities and their products are homogeneous. Using games to such a mixed quantity duopoly market a main question is to decide which kind of games and equilibria should be considered, here: simultaneous (Cournot) or sequential (Stackelberg) game. The authors show, that this decision and also, who is leader or follower in the Stackelberg case, can be determined endogenously adding a preplay to the duopoly game in the sense as in [\textit{J. H. Hamilton} and \textit{S. M. Slutsky}, Games Econ. Behav. 2, No. 1, 29--46 (1990; Zbl 0753.90074)]. Then, under certain assumptions, it is proved, that the wanted decision is Stackelberg game, and -- as the authors write -- the most plausible outcome is public leadership, when the private firm is foreign, and public or private leadership, when the private firm is domestic. The conclusion of the paper also gives a lot of hints from the economic point of view, e.g. on the effect of privatization. From the mathematical point of view the stated assumptions for this part of game theory are interesting: only pure strategies are dealt with, the inverse demand function has esp. to be twice continuously differentiable, the cost functions also and they must be increasing, sometimes (f.i. in Theorem 5) convex, an interiority assumption on simultaneously-move equilibria must hold. A big appendix contains proofs using the mentioned assumptions and the smooth implicit function theorem, the envelope theorem and Dini derivatives together with results of the theory of supermodular games.
reviewed by: Alfred Göpfert
Mathematics Subject Classification ID: 91B54
Mathematics Subject Classification ID: 91B52
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 91A55
Mathematics Subject Classification ID: 91A65
Mathematics Subject Classification ID: 91A80
zbMATH DE Number: 6336297
zbMATH Keywords: mixed duopoly market
zbMATH Keywords: endogenous timing
zbMATH Keywords: Cournot equilibrium
zbMATH Keywords: Stackelberg equilibrium
zbMATH Keywords: supermodular game
zbMATH Keywords: welfare maximizing firm
zbMATH Keywords: profit maximizing firm
MaRDI profile type: Publication
OpenAlex ID: W2157842238
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DOI: 10.1007/S00182-013-0401-Y
description: scientific article; zbMATH DE number 6336297