Multiple-Object Auctions:

In a multiple-identical-object auction, every bidder tries to win as many objects as possible with a randomized bidding algorithm. In this proposal we would like to study  position-randomized auctions, which form a special class of multiple-identical-object auctions where a randomized 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 randomized bidding algorithms of others. For the case of only two bidders, we have some preliminary result showing an optimal randomized bidding algorithm for the disadvantaged bidder. This initial 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. We would like to further investigate some basic issues of multiple-identical-object auctions, including (1) information advantage, (2) bidding with collusion, and (3) the case with more than two bidders.