Upper Bound for the Competitive Facility Location Problem with Quantile Criterion

In this paper, we consider a competitive location problem in a form of Stackelberg game. Two parties open facilities with the goal to capture customers and maximize own profits. One of the parties, called Leader, opens facilities first. The set of customers is specified after Leader's turn with random realization of one of possible scenarios. Leader's goal is to maximize the profit guaranteed with given probability or reliability level provided that the second party, called Follower, acts rationally in each of the scenarios. We suggest an estimating problem to obtain an upper bound for Leader's objective function and compare the performance of estimating problem reformulations experimentally.