Customized bundle pricing for information goods: A nonlinear mixed-integer programming approach

This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers' profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes evert when exact consumer valuations are not known ex ante.