Optimal Item Pricing in Online Combinatorial Auctions

We consider a fundamental pricing problem in combinatorial auctions. are given set of indivisible items and buyers with randomly drawn monotone valuations over subsets items. A decision maker sets item prices then the make sequential purchasing decisions, taking their favorite among remaining parametrize an instance by d, size largest buyer may want. Our main result asserts that there exist such expected (over random valuations) welfare allocation they induce is at least factor $$1/(d+1)$$ times optimal hindsight. Moreover we prove this bound tight. Thus, our not only improves upon $$1/(4d-2)$$ Dütting et al., but also settles approximation can be achieved using prices. further show how to compute polynomial time. provide additional results for special case when buyers’ known (but posted-price mechanism still desired).