A gradient descent algorithm for computing choice probability in the bundle size pricing problem

Bundle size pricing has important applications in the service industry, TV and film, media, and other industries and so has been widely studied. In this paper, we prove that the objective function of the cross-moment model of the bundle size pricing problem is strongly convex and the gradient is Lipschitz continuous in the constrained region. Based on this property, we propose a gradient descent algorithm to compute choice probability by solving this model. Moreover, we prove that the proposed algorithm is linearly convergent. Numerical experiments verify the effectiveness of the algorithm and the accuracy of the cross-moment model for the choice probability estimation.