Abstract
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.
REFERENCES
K. Bimpikis, S. Ehsani, and R. \( \dot {\mathrm {I}} \)lkılıç, “Cournot competition in networked markets,” Manage. Sci. 65 (6), 2467–2481 (2019).
N. Jabarzare and M. Rasti-Barzoki, “A game theoretic approach for pricing and determining quality level through coordination contracts in a dual-channel supply chain including manufacturer and packaging company,” Int. J. Prod. Econ. 221, 107480 (2020).
V. Nocke and N. Schutz, “Multiproduct-firm oligopoly: An aggregative games approach,” Econometrica, 86 (2), 523–557 (2018).
C. E. Caspi, J. E. Pelletier, L. J. Harnack, D. J. Erickson, K. Lenk, and M. N. Laska, “Pricing of staple foods at supermarkets versus small food stores,” Int. J. Environ. Res. Public Health 14 (8), 915 (2017).
B. Minten and T. Reardon, “Food prices, quality, and quality’s pricing in supermarkets versus traditional markets in developing countries,” Appl. Econ. Perspect. Policy 30 (3), 480–490 (2008).
T. Reardon, R. Echeverria, J. Berdegue, B. Minten, S. Liverpool-Tasie, D. Tschirley, and D. Zilberman, “Rapid transformation of food systems in developing regions: Highlighting the role of agricultural research and innovations,” Agric. Syst. 172, 47–59 (2019).
J. A. Cook and F. Gale, “Using food prices and consumption to examine Chinese cost of living,” Pac. Econ. Rev. 24 (1), 3–26 (2019).
L. Briceno-Arias, J. R. Correa, and A. Perlroth, “Optimal continuous pricing with strategic consumers,” Manage. Sci. 63 (8), 2741–2755 (2017).
M. Choi, A. Y. Dai, and K. Kim, “Consumer search and price competition,” Econometrica 86 (4), 1257–1281 (2018).
W. Cui and L. Li, “A game-theoretic approach to optimize the Time-of-Use pricing considering customer behaviors,” Int. J. Prod. Econ. 201, 75–88 (2018).
D. Martin, “Strategic pricing with rational inattention to quality,” Games Econ. Behav. 104, 131–145 (2017).
M. Babaioff, S. Dughmi, R. Kleinberg, and A. Slivkins, “Dynamic pricing with limited supply,” ACM Trans. Econ. Comput. 3 (1), 1–26 (2015).
J. Chen, J. Jian, and S. Hong, “Quantum repeated pricing game,” Quantum Inf. Process. 19 (2), 42 (2020).
K. P. Rath, “Stationary and nonstationary strategies in Hotelling’s model of spatial competition with repeated pricing decisions,” Int. J. Game Theory 27 (4), 525–537 (1998).
D. Monderer and L. S. Shapley, “Potential games,” Games Econ. Behav. 14 (1), 124–143 (1996).
V. V. Gusev, “Nash-stable coalition partition and potential functions in games with coalition structure,” Eur. J. Oper. Res. 295 (3), 1180–1188 (2021).
R. W. Rosenthal, “A class of games possessing pure-strategy Nash equilibria,” Int. J. Game Theory 2 (1), 65–67 (1973).
I. Milchtaich, “Congestion games with player-specific payoff functions,” Games Econ. Behav. 13 (1), 111–124 (1996).
L. Li and Y. S. Lee, “Pricing and delivery-time performance in a competitive environment,” Manage. Sci. 40 (5), 633–646 (1994).
G. S. Crawford, N. Pavanini, and F. Schivardi, “Asymmetric information and imperfect competition in lending markets,” Am. Econ. Rev. 108 (7), 1659–1701 (2018).
L. Mitridati, J. Kazempour, and P. Pinson, “Design and Game-theoretic analysis of community-based market mechanisms in heat and electricity systems,” Omega , 102177 (2019).
X. Xu, R. Chen, and L. Jiang, “The influence of payment mechanisms on pricing: when mental imagery stimulates desire for money,” J. Retail. 96 (2), 178–188 (2020).
Funding
This research was supported by the Russian Science Foundation, project no. 22–21–20070, and a grant from the St. Petersburg Science Foundation under Agreement no. 65/2022 of April 15, 2022.
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Translated by V. Potapchouck
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Gusev, V.V. Pure Nash Equilibrium in a Two-Step Pricing Game: Covering a Tourist City with Retail Outlets. J. Appl. Ind. Math. 17, 72–85 (2023). https://doi.org/10.1134/S199047892301009X
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DOI: https://doi.org/10.1134/S199047892301009X