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Irrelevance of the choice of strategic variables in duopoly under relative profit maximization

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  • Tanaka, Yasuhito

Abstract

We study the choice of strategic variables by firms in a duopoly in which two firms produce differentiated substitutable goods and each firm maximizes its relative profit that is the difference between its profit and the profit of the rival firm. We consider a two stage game such that in the first stage the firms choose their strategic variables and in the second stage they determine the values of their strategic variables. We show that when the firms maximize their relative profits, the choice of strategic variables is irrelevant to the outcome of the game in the sense that the equilibrium outputs, prices and profits of the firms are the same in all situations, and so any combination of strategy choice by the firms constitutes a sub-game perfect equilibrium in the two stage game. We assume that demand functions for the goods are symmetric and linear, the marginal costs of the firms are common and constant, and the fixed costs are zero.

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  • Tanaka, Yasuhito, 2014. "Irrelevance of the choice of strategic variables in duopoly under relative profit maximization," MPRA Paper 55891, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:55891
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    References listed on IDEAS

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    More about this item

    Keywords

    duopoly; relative profit maximization; choice of strategic variables;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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