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

Tanaka, Yasuhito (2014): Irrelevance of the choice of strategic variables in duopoly under relative profit maximization. Published in:

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: duopoly, relative profit maximization, choice of strategic variables
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection

References

Bolton, G.E. and A. Ockenfels (2000), ``A theory of equity, reciprocity, and competition'', American Economic Review 90, 166-193.

Gibbons, R and K. J. Murphy (1990), ``Relative performance evaluation for chief executive officers'', Industrial and Labor Relations Review, 43, 30S–51S.

Kockesen, L., E.A. Ok and R. Sethi (2000), ``The strategic advantage of negatively interdependent preferences'', Journal of Economic Theory 92, 274-299.

Lundgren, C. (1996), ``Using relative profit incentives to prevent collusion'', Review of Industrial Organization 11, 533-550.

Matsumura, T., N. Matsushima and S. Cato (2009), ``Relative Performance and R\&D Competition'', ISER Discussion Paper 0752, Institute of Social and Economic Research, Osaka University.

Schaffer, M.E. (1989), ``Are profit maximizers the best survivors?'', Journal of Economic Behavior and Organization 12, 29-–45.

Tanaka, Y. (2013), ``Equivalence of Cournot and Bertrand equilibria in differentiated duopoly under relative profit maximization with linear demand'', mimeograph.

Vega-Redondo, F. (1997), ``The evolution of Walrasian behavior'', Econometrica 65, 375-384.