This year-long project resulted in 6 papers appearing in 1st-tier scientific venues. The results are of two kinds:
-Extending the mathematical and computational theory of complements
-Applications to the design of better computational markets
Both branches of results have been presented to interdisciplinary researchers (from computing, engineering, economics, management science and business disciplines) in multiple international forums, as well as to industry players like Microsoft and to public policy makers.
In the first branch, our research has uncovered intriguing mathematical structure. To give an idea of our results in a nutshell, consider a simple analogue of the complex valuation function that every market player has for owning different combinations of goods: a one-dimensional function f(x)=y. It is well known that if the function is concave (“hill shaped”), it is computationally easy to find its maximum, while for an arbitrary non-concave function, simple algorithms might get stuck at a suboptimal point. We are interested in the intermediate case, where the function is “approximately” concave – this is the analogue of a market with limited complements (it is “approximately” complement-free). Adding noise to a concave function maintains approximate concavity, but for the mathematical objects we are dealing with – high dimensional discrete functions – establishing this is challenging, and our result was recognized by the community as “one of the best results in algorithms published in the last year”. It may be a first step in establishing that noisy, real-life markets are approximately complement-free. However, we also find that many standard techniques like greedy or ascending auctions may fail miserably with even a small dose of complements – not an acceptable risk e.g. in high-stake spectrum auctions. This motivates further research to design more robust market mechanisms.
In the second branch, on the applications side, we develop more robust market mechanisms for: (1) extracting revenue (the driving force behind the internet and sharing economies), and (2) fairness and social good. For revenue, our mechanisms are based on simple and practical methods rather than on complex, personalized and dynamic pricing methods. Namely, we show that the following methods are robust to a mild degree of complements and yield high revenue: (a) taking the best of selling goods separately and bundling them together; (b) enhancing competition for the goods (e.g. by investing in advertising). For social good and fairness, we analyze a method based on artificial currency: for example, students enrolling in over-demanded courses get “budgets” depending on their year of study, academic performance, etc., and use these budgets to “shop” for courses whose “price” reflects their popularity. Besides being transparent, we show this method has nice fairness guarantees. It is applicable to many scenarios, from sharing a family heirloom to allocating cabinet ministries among political parties.
