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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 15.02.2021
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
Linking options:
https://www.mathnet.ru/eng/iimi415 https://www.mathnet.ru/eng/iimi/v57/p170
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