Optimal Bid Sequences for Multiple-Object Auctions with Unequal Budgets

Details Optimal Bid Sequences for Multiple-Object Auctions with Unequal Budgets Optimal Bid Sequences for Multiple-Object Auctions with Unequal Budgets

2001-02-10

arxiv.org/abs/cs/0102008v1

Computer Science

Computational Engineering, Finance, and Science

A preliminary version appeared in In D. T. Lee and S. H. Teng, editors, Lecture Notes in Computer Science 1969: Proceedings of

Scientific paper

In a multiple-object auction, every bidder tries to win as many objects as possible with a bidding algorithm. This paper studies position-randomized auctions, which form a special class of multiple-object auctions where a bidding algorithm consists of an initial bid sequence and an algorithm for randomly permuting the sequence. We are especially concerned with situations where some bidders know the bidding algorithms of others. For the case of only two bidders, we give an optimal bidding algorithm for the disadvantaged bidder. Our result generalizes previous work by allowing the bidders to have unequal budgets. One might naturally anticipate that the optimal expected numbers of objects won by the bidders would be proportional to their budgets. Surprisingly, this is not true. Our new algorithm runs in optimal O(n) time in a straightforward manner. The case with more than two bidders is open.

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