Pure Nash Equilibrium in a Two-Step Pricing Game: Covering a Tourist City with Retail Outlets

Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций"). 2023. Vol. 17. No. 1. P. 72–85.

Gusev V.

Small business in small tourist cities is aimed at meeting the needs of visiting tourists; therefore, competition is formed between entrepreneurs from one area of service provision, making the pricing problem relevant. Some entrepreneurs need to decide on the cost of their product and the place of its sale. If, due to competition, an individual entrepreneur often changes the place of sale of his goods, then he/she might skip the season and not get the desired profit. Of interest is the case where the place of sale is chosen based on pure strategies. Using the concept of congestion games with player-specific payoff functions and the theory of ordinal potential functions, we show the existence of an equilibrium in the pricing game. As an example, an equilibrium distribution of individual entrepreneurs by retail outlets in the city of Gelendzhik is found.

Keywords: теория игр, game theory, potential games, pure Nash equilibrium, pricing game, чистое равновесие Нэша, игра ценообразования, потенциальные игры