A retailer is purchasing goods in bundles from suppliers and then selling these goods in bundles to customers; her goal is to maximize profit, which is the revenue obtained from selling goods minus the cost of purchasing those goods. In this paper, we study this general trading problem from the retailer's perspective, where both suppliers and customers arrive online. The retailer has inventory constraints on the number of goods from each type that she can store, and she must decide upon arrival of each supplier/customer which goods to buy/sell in order to maximize profit. We design an algorithm with logarithmic competitive ratio compared to an optimal offline solution. We achieve this via an exponential-weight-update dynamic pricing scheme, and our analysis dual fits the retailer's profit with respect to a linear programming formulation upper bounding the optimal offline profit. We prove (almost) matching lower bounds, and we also extend our result to an incentive compatible mechanism. Prior to our work, algorithms for trading bundles were known only for the special case of selling an initial inventory.
Azar et al. (Wed,) studied this question.