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 Izv. IMI UdGU, 2021, Volume 57, Pages 170–180 (Mi iimi415)

MATHEMATICS

Game with a random second player and its application to the problem of optimal fare choice

G. A. Timofeevaab, D. S. Zavalishchinac

a Ural State University of Railway Transport, ul. Kolmogorova, 66, Yekaterinburg, 620034, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
c N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620108, Russia

Abstract: The choice of the optimal strategy for a significant number of applied problems can be formalized as a game theory problem, even in conditions of incomplete information. The article deals with a hierarchical game with a random second player, in which the first player chooses a deterministic solution, and the second player is represented by a set of decision makers. The strategies of the players that ensure the Stackelberg equilibrium are studied. The strategy of the second player is formalized as a probabilistic solution to an optimization problem with an objective function depending on a continuously distributed random parameter. In many cases, the choice of optimal strategies takes place in conditions when there are many decision makers, and each of them chooses a decision based on his (her) criterion. The mathematical formalization of such problems leads to the study of probabilistic solutions to problems with an objective function depending on a random parameter. In particular, probabilistic solutions are used for mathematical describing the passenger's choice of a mode of transport. The problem of optimal fare choice for a new route based on a probabilistic model of passenger preferences is considered. In this formalization, the carrier that sets the fare is treated as the first player; the set of passengers is treated as the second player. The second player's strategy is formalized as a probabilistic solution to an optimization problem with a random objective function. A model example is considered.

Keywords: hierarchical game, Stackelberg equilibrium, random second player, probabilistic solution, route selection, optimal fare.

 Funding Agency Grant Number The study was funded by federal budget of the Russian Federation within the framework of the state order, the project “Optimization of the transport and logistics system based on modeling the development of transport infrastructure and models of consumer preference”.

DOI: https://doi.org/10.35634/2226-3594-2021-57-08

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Bibliographic databases:

UDC: 519.83
MSC: 91A27, 91A65

Citation: G. A. Timofeeva, D. S. Zavalishchin, “Game with a random second player and its application to the problem of optimal fare choice”, Izv. IMI UdGU, 57 (2021), 170–180

Citation in format AMSBIB
\Bibitem{TimZav21} \by G.~A.~Timofeeva, D.~S.~Zavalishchin \paper Game with a random second player and its application to the problem of optimal fare choice \jour Izv. IMI UdGU \yr 2021 \vol 57 \pages 170--180 \mathnet{http://mi.mathnet.ru/iimi415} \crossref{https://doi.org/10.35634/2226-3594-2021-57-08}