General framework of opening and closing shops over a spatial network based on stochastic utility under competitive and time-bounded environment

Abstract

We propose a general framework of opening and closing shops in group competitive environment, i.e., shops in the same group work cooperatively and those in different groups competitively, based on stochastic utility which is given by a function of shop distance and attractiveness with an explicit traveling time-bound imposed. The framework allows to derive a specific prediction model by choosing a specific function form of utility, including the one we propose, its variants and the conventional state-of-the-art gravity model which we chose as a reference. We compute a marginal gain of the market share which is derived from the utility function and the consumers buying power as a measure to rank the candidate location. Using the real dataset of three convenience store groups in four cities in Japan, we analyzed how the derived models behave with respect to the time-bound and the other parameters and how each model compare with others. We confirm that, despite the simplification we made in the model, inferred rankings of the shops newly opened in the real data are shown to be high implying that our prediction model and other variants are reasonable. We show that our model gives much more realistic results than the gravity model, which indicates that our group competitive mechanism with the time-bounded stochastic utility is vital and promising. Inclusion of the time-bound constraint is crucially important. Analyses of the dynamics of opening and closing shops indicate that competition indeed affects the market share of each group over time, and the total share eventually increases although small, and the difference of the share within each group gradually becomes smaller, revealing that the spatial distribution of the shops in each group becomes more uniform.