Bid Determination in Simultaneous Auctions

In this paper, bid determination problems are studied. In particular, the central problems of allocation, acquisition, completion, and arbitrage are defined. The main theoretical result states that bid determination in double-sided auctions—i.e., completion—where goods can be sold as well as bought, is polynomial-time reducible to bid determination in single-sided auctions—i.e., acquisition. Such problems are faced by autonomous agents trading in simultaneous auctions. Regarding complexity, it is noted that allocation in simultaneous auctions is formally equivalent to winner determination in combinatorial auctions. Since the winner determination problem is NP-hard [8], and since completion generalizes acquisition, which in turn generalizes allocation, it follows that all three of these bid determination problems are NP-hard. Consequently, we advocate the use of heuristic search methods to solve bid determination problems. Two algorithmic approaches to bid determination are studied here, inspired by the two topscoring TAC–2000 agents. These alternatives are compared experimentally using data from TAC– 2000. Three experimental findings are reported: (i) for the dimensions of TAC–2000, optimal solutions are tractable; (ii) optimal solutions do not scale; (iii) heuristic approximation methods scale well, achieving near optimal solutions with predictable time and space requirements.