A competitive inventory model with the customer's general choice probability

We consider a single-period model with reallocation of excess demand such that two firms offer some product for customers who are uniformly distributed on a line segment market. This model results in one of the unit square games with pure strategies of continuous cardinality. Their purposes are to find the optimal ordering quantity that minimizes the total cost. We generate a matrix by arranging the ordering quantity obtained in the usual way as one of the strategies for each player and analyze our model in a way to find an equilibrium pair.