Efficient computation of discrete games: Estimating the effect of Apple on market structure

Abstract

Discrete games provide the means to analyze market dynamics with limited data. However, computing such games with many players—especially in a complete information setting—is computationally infeasible because the strategy space increases exponentially with the number of players. This study presents a novel and practical method to compute and estimate discrete games. To do so, the study introduces two methodological innovations. First, we develop an efficient simulator that requires fewer random draws to evaluate the likelihood of discrete games with multiple equilibria. The augmented simulator avoids random draws that are not compatible with the observed equilibrium outcome and, thus, efficiently uses all draws to evaluate the likelihood. Second, we utilize general‐purpose computing on graphics‐processing unit (GPGPU), using multiple processing cores in a graphics‐processing unit, to increase computational speed. The two features allow us to estimate the model significantly faster compared to traditional methods. The study's empirical application examines the effect of Apple's company‐owned stores on the retail market structure. The results show that agglomeration effects exist between Apple and upscale firms. The presence of an Apple store attracts high‐income customers, promoting the entry of upscale firms and the exit of discount firms.