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Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets

Yulia Dzhabarova (), Stanimir Kabaivanov (), Margarita Ruseva () and Boyan Zlatanov ()
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Yulia Dzhabarova: Department of Marketing and International Economic Relations, Faculty of Economics and Social Sciences, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria
Stanimir Kabaivanov: Department of Finance and Accounting, Faculty of Economics and Social Sciences, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria
Margarita Ruseva: Department of Management and Quantitative Economicsx, Faculty of Economics and Social Sciences, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria
Boyan Zlatanov: Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria

Administrative Sciences, 2020, vol. 10, issue 3, 1-32

Abstract: In this paper we build a pragmatic model on competition in oligopoly markets. To achieve this goal, we use an approach based on studying the response functions of each market participant, thus making it possible to address both Cournot and Bertrand industrial structures with a unified formal method. In contrast to the restrictive theoretical constructs of duopoly equilibrium, our study is able to account for real-world limitations like minimal sustainable production levels and exclusive access to certain resources. We prove and demonstrate that by using carefully constructed response functions it is possible to build and calibrate a model that reflects different competitive strategies used in extremely concentrated markets. The response functions approach makes it also possible to take into consideration different barriers to entry. By fitting to the response functions rather than the profit maximization of the payoff functions problem we alter the classical optimization problem to a problem of coupled fixed points, which has the benefit that considering corner optimum, corner equilibria and convexity condition of the payoff function can be skipped.

Keywords: duopoly equilibrium; response functions; imperfect competition; entry barriers (search for similar items in EconPapers)
JEL-codes: M M0 M1 M10 M11 M12 M14 M15 M16 L (search for similar items in EconPapers)
Date: 2020
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