Sponsored search auction has been recently studied and auctioneer's revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization prob...Sponsored search auction has been recently studied and auctioneer's revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization problem on different methods to bundle contexts. In this paper, we propose a more flexible and natural method which is called the bracketing method. We prove that finding a bracketing scheme that maximizes the auctioneer's revenue is strongly NP-hard. Then, a heuristic algorithm is given. Experiments on three test cases show that the revenue of the optimal bracketing scheme is very close to the optimal revenue without any bundling constraint, and the heuristic algorithm performs very well. Finally, we consider a simpler model that for each row in the valuation matrix, the non-zero cells have the same value. We prove that the revenue maximization problem with Kanonymous signaling scheme and cardinality constrained signaling scheme in this simpler model are both NP-hard.展开更多
基金the National Natural Science Foundation of China (Grant No. 61672012).
文摘Sponsored search auction has been recently studied and auctioneer's revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization problem on different methods to bundle contexts. In this paper, we propose a more flexible and natural method which is called the bracketing method. We prove that finding a bracketing scheme that maximizes the auctioneer's revenue is strongly NP-hard. Then, a heuristic algorithm is given. Experiments on three test cases show that the revenue of the optimal bracketing scheme is very close to the optimal revenue without any bundling constraint, and the heuristic algorithm performs very well. Finally, we consider a simpler model that for each row in the valuation matrix, the non-zero cells have the same value. We prove that the revenue maximization problem with Kanonymous signaling scheme and cardinality constrained signaling scheme in this simpler model are both NP-hard.
