Analyses of location-price game on networks with stochastic customer behavior and its heuristic algorithm

In this paper, a two-stage model is developed to investigate the location strategy and the commodity pricing strategy for a retail firm that wants to enter a spatial market with multiple competitive facilities, where a competitor firm is already operating as a monopoly with several outlets. Expected market shares are calculated based on the stochastic customer behavior on networks. The authors provide a sufficient condition for the existence of equilibrium prices in the price game for the first time. The existence and uniqueness of the pure strategy Nash equilibrium price with a specified utility function are proved in the subgame. A metaheuristic based on tabu search is proposed to search the optimal location-price solution of the model. In addition, the authors provide two numerical examples to illustrate how to obtain the optimal solution and conduct sensitivity analysis. The analysis shows that the best location decision is robust for the follower firm, price game is more intense when incomes of consumers are lower or there are more substitution products, and neither chain retail gains from the price competition.