Abstract: We consider a mathematical model of decision making by a company attempting to win a market share. We assume that the company releases its products to the market under the competitive conditions that another company is making similar products. Both companies can vary the kinds of their products on the market as well as the prices in accordance with consumer preferences. Each company aims to maximize its profit. A mathematical statement of the decisionmaking problem for the market players is a bilevel mathematical programming problem that reduces to a competitive facility location problem. As regards the latter, we propose a method for finding an upper bound for the optimal value of the objective function and an algorithm for constructing an approximate solution. The algorithm amounts to local ascent search in a neighborhood of a particular form, which starts with an initial approximate solution obtained simultaneously with an upper bound. We give a computational example of the problem under study which demonstrates the output of the algorithm.

Cite: Beresnev V.L. , Suslov V.I.
A Mathematical Model of Market Competition
Journal of Applied and Industrial Mathematics. 2010. V.2. N1. P.1-11. DOI: 10.1134/S1990478910020018 Scopus OpenAlex

Original: Береснев В.Л. , Суслов В.И.
Математическая модель конкурентной борьбы на рынке
Сибирский журнал индустриальной математики. 2009. Т.12. №1. С.11-24.

Identifiers:

Scopus:	2-s2.0-77953486145
OpenAlex:	W2047066213

Citing: Пока нет цитирований

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