The Equivalence of Bundling and Advance Sales

We identify the conditions under which a problem of optimal advance selling strategy can be mathematically transformed into a problem of optimal bundle pricing. These conditions are as follows: (i) consumers and sellers have common priors on the probability of each state being realized in the future, (ii) consumers are risk-neutral, (iii) sellers can commit to spot prices, and (iv) consumers and sellers discount the future at the same rate. The result allows both researchers and practitioners to extend and/or apply the findings from the vast literature on bundling to advance selling problems, and vice versa. We highlight several insights that are particularly relevant, such as the importance of the dependence of consumer valuations across states on the profitability of advance selling in the base case of two states as well as in the cases of more than two states or with possible competition in some of the states.