Opening and Closing Dynamics of Competing Shop Groups over Spatial Networks

We address the problem of opening and closing shops in group competitive environment, i.e., shops in the same group work cooperatively and those in different groups competitively, and analyze how the market share and location changes over time. We formulate a stochastic utility of each shop as a function of shop distance and attractiveness from which a market share is computed by weighting consumers buying power. We further place a constraint on the traveling time, which is crucial to reduce the computation time, and use a marginal gain of the market share as a measure to rank the candidate location. Using the real dataset of three convenience stores in four cities in Japan, we confirm that, despite the simplification we made in the model, rankings of the existing shops are shown to be high which implies that our model is reasonable. Further, comparison with the baseline gravity model shows that our model gives much more realistic results. Analyses of the dynamics of opening and closing shops indicate that the reasonable time-bound for walking is about 10 min., the market share of each group, thus 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.