A competitive inventory model with reallocation on a plane market

This paper considers a duopolistic inventory model with reallocation. Customers move according to the rectilinear distance over a plane market and choose a player whom they first visit with a probability dependent on their positions. This model can be interpreted as one of the unit-square games with pure strategies of continuous cardinary. We consider the optimal strategies for two players from a viewpoint of pure strategies. The purpose of this paper is concretely to find an equilibrium point with respect to the optimal ordering quantities which minimize the total costs by using a payoff bimatrix in the deterministic model and to find the optimal solution in the stochastic model. As can be seen in this paper, there is a unique equilibrium point.