Non-Cooperative Bundling Games

Bundling is a basic problem in commerce. We define and study the Bundling Game: each of n players with a unique product to sell can choose to sell their products in bundles with other players’ products so as to maximize their payoff; the players all have knowledge of the valuations of m (potential) buyers for each of the products. We define two natural classes of payoff functions Fair Profit Sharing Functions (FPSFs) and Incentive Functions (IFs). For the former we prove the surprising impossibility result that there exists no FPSF that can always guarantee stability (a pure Nash equilibrium). We counterbalance this result by showing that pure Nash equilibria always exist for IFs and obtain tight bounds on the Price of Anarchy. Motivated by the bundling game, we present hardness results and approximation algorithms for the optimization problems of finding revenue maximizing bundlings and bundles, and associated variants.