Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior

Stanislav Stoykov () and Ivan Kostov
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Stanislav Stoykov: FactSet Research Systems Inc., 43 Glover Ave. Fl. 7, Norwalk, CT 06850, USA
Ivan Kostov: Management Board of the Center for Analyzes and Risk Management, New Bulgarian University, ul. “Montevideo” 21, g.k. Ovcha Kupel 2, 1618 Sofia, Bulgaria

Games, 2023, vol. 14, issue 2, 1-25

Abstract: A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences of consumers were included in the model. Firms implement two strategies in the market: profit maximization and market share maximization. Numerical discretization of a two-dimensional area was performed for computing the equilibrium prices which allows one to consider any market area and any location of the firms. Four scenarios of oligopoly markets were developed by combining both strategies from one side and competitive behavior and a partial cartel agreement from another side. The main differences between the scenarios are outlined. Profits, market shares and equilibrium prices are presented and compared. The influence of collusion, the existence of participants with a market share maximization strategy and consumer preferences on the firm’s profits and equilibrium prices were examined. Cases whereby firms prefer to leave the cartel were investigated. Best locations for the setting of a new store for profit maximization are shown and discussed.

Keywords: Bertrand competition; collusive agreement; consumer preferences; oligopoly market; Voronoi diagrams (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2023
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