Optimal Bid Sequences for Multiple-Object Auctions with Unequal Budgets

Title: Optimal Bid Sequences for Multiple-Object Auctions with Unequal Budgets

Abstract: This research study focuses on the problem of multiple-object auctions, where each bidder tries to win as many objects as possible with a bidding algorithm. The study specifically examines position-randomized auctions, 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. The researchers are particularly concerned with situations where some bidders know the bidding algorithms of others. They provide an optimal bidding algorithm for the disadvantaged bidder in the case of only two bidders, generalizing previous work that allowed bidders to have unequal budgets. The algorithm runs in optimal O(n) time and is applicable to situations where bidders have unequal budgets. The case with more than two bidders remains open.

Main Research Question: How can bidders in a multiple-object auction with unequal budgets develop an optimal bidding algorithm to maximize their chances of winning objects, especially when some bidders know the algorithms of others?

Methodology: The researchers use a combination of mathematical modeling, algorithm development, and computational analysis to address the research question. They start by defining the problem and the assumptions, including the number of bidders and objects, each bidder's budget, and the knowledge of bidding algorithms among bidders. They then develop an optimal bidding algorithm for the disadvantaged bidder in the case of only two bidders, which generalizes previous work. The algorithm runs in optimal O(n) time and is applicable to situations where bidders have unequal budgets.

Results: The study provides an optimal bidding algorithm for the disadvantaged bidder in the case of only two bidders, generalizing previous work that allowed bidders to have unequal budgets. The algorithm runs in optimal O(n) time and is applicable to situations where bidders have unequal budgets.

Implications: The research has implications for the field of computer science and auction theory. It provides a new approach to developing bidding algorithms for multiple-object auctions, especially when bidders have unequal budgets and some bidders know the algorithms of others. The study also contributes to the ongoing research on the computational complexity of auction and the informational security of auction, two important themes in the field.

Link to Article: https://arxiv.org/abs/0102008v1 Authors: arXiv ID: 0102008v1