Hierarchical game with random second player and its application

Abstract

A hierarchical game with a random second player is considered, optimal strategies are defined on the base of Stackelberg equilibrium. The random second player is understood as a randomly selected person from a homogeneous set of decision-makers. The proposed model can be used in various problems. First of all, it is may be used for optimal price choosing for a new product. In the article the model is applied to the problem of setting the optimal fare to a new route. A carrier acts as a first player, a randomly selected passenger acts as a second player. It is assumed that the function of passenger's preferences depends on a random parameter. The price for the hierarchical game is an optimal payoff of the first player, this price is compared with the price of a game in which the strategies of both players depend on a random parameter. A model example is considered.