Geodesic
Game with a random second player and its application to the problem of optimal fare choice
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 170-180.

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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, optimal fare.
Mots-clés : probabilistic solution, route selection 
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G. A. Timofeeva; D. S. Zavalishchin. Game with a random second player and its application to the problem of optimal fare choice. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 170-180. http://geodesic.mathdoc.fr/item/IIMI_2021_57_a7/

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