预算不等的多目标拍卖的最优投标序列
Optimal Bid Sequences for Multiple-Object Auctions with Unequal Budgets
摘要：
在多物品拍卖中，每个出价人都试图通过出价算法赢得尽可能多的物品。本文研究了位置随机拍卖，它形成了一类特殊的多物品拍卖，其中投标算法由初始投标序列和随机排列序列的算法组成。我们特别关注的情况下，一些投标人知道别人的投标算法。对于只有两个投标人的情况，我们给出了一个处于劣势的投标人的最优投标算法。我们的结果概括了以前的工作，允许投标人有不平等的预算。人们可能会自然地预期，投标人赢得的物品的最佳预期数量将与他们的预算成比例。令人惊讶的是，这不是真的。我们的新算法以一种简单的方式在最优O（n）时间内运行。有两个以上投标人的情况是开放的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
