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Using robust optimisation to solve multi-item pricing problems

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Published on Thursday, 28 January 2021

Mathematical Programming, a top-core journal in TISEM list, has recently featured Assistant Prof. Çağıl Koçyiğit’s latest research on multidimensional pricing. The article “Robust Multidimensional Pricing: Separation without Regret” studies robust multi-item pricing problems over deterministic and randomised sales mechanisms from a mathematical optimisation perspective.

The multi-item pricing problem where multiple items are offered to a single buyer is very difficult because the seller can bundle items into subsets and try to sell them together to increase his or her profit. Unfortunately, the number of possible bundles is exponential in the number of items. Moreover, the seller can even randomise the allocation of items to bundles and randomise the bundle prices. Thus, the set of available sales mechanisms is very rich. In fact, if the distribution of the buyer's values for the items is known, then the revenue maximisation problem of the seller is known to be #P-hard even in the simplest settings.

In a collaboration with Prof. Napat Rujeerapaiboon from the National University of Singapore and Prof. Daniel Kuhn from École polytechnique fédérale de Lausanne, Prof. Çağıl Koçyiğit studies the multi-item pricing problem from a robust optimisation perspective, postulating that the buyer’s values may follow any distribution on a given rectangular uncertainty set. Under this assumption, the authors identify an explicit analytical solution to the mechanism design problem of the seller who wishes to minimise his or her regret. The optimal randomised mechanism as well as the optimal deterministic mechanism sell the goods separately. The main results of the paper thus motivate separate sales of items under lack of information about the demand, which is typically the case for new products.

The paper uses original techniques from robust optimisation. The authors hope that similar techniques can be applied to solve different distributionally robust mechanism design problems.  

The paper is available at:

http://dx.doi.org/10.1007/s10107-021-01615-4