### Online algorithms for market clearingOnline algorithms for market clearing

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 Author Blum, Avrim ♦ Sandholm, Tuomas ♦ Zinkevich, Martin Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2006 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Competitive analysis ♦ Double auctions ♦ Exchanges ♦ Online algorithms Abstract In this article, we study the problem of online market clearing where there is one commodity in the market being bought and sold by multiple buyers and sellers whose bids arrive and expire at different times. The auctioneer is faced with an online clearing problem of deciding which buy and sell bids to match without knowing what bids will arrive in the future. For maximizing $\textit{profit},$ we present a (randomized) online algorithm with a competitive ratio of $ln(p_{max}$ ™ $p_{min})$ + 1, when bids are in a range $[p_{min},$ $p_{max}],$ which we show is the best possible. A simpler algorithm has a ratio twice this, and can be used even if expiration times are not known. For maximizing the $\textit{number}$ of trades, we present a simple greedy algorithm that achieves a factor of 2 competitive ratio if no money-losing trades are allowed. We also show that if the online algorithm is allowed to $\textit{subsidize}$ matches---match money-losing pairs if it has already collected enough money from previous pairs to pay for them---then it can actually be 1-competitive with respect to the optimal offline algorithm that is not allowed subsidy. That is, for maximizing the number of trades, the ability to subsidize is at least as valuable as knowing the future. We also consider objectives of maximizing buy or sell volume and social welfare. We present all of these results as corollaries of theorems on online matching in an incomplete interval graph.We also consider the issue of incentive compatibility, and develop a nearly optimal incentive-compatible algorithm for maximizing social welfare. For maximizing $\textit{profit},$ we show that no incentive-compatible algorithm can achieve a sublinear competitive ratio, even if only one buy bid and one sell bid are alive at a time. However, we provide an algorithm that, under certain mild assumptions on the bids, performs nearly as well as the best fixed pair of buy and sell prices, a weaker but still natural performance measure. This latter result uses online learning methods, and we also show how such methods can be used to improve our “optimal” algorithms to a broader notion of optimality. Finally, we show how some of our results can be generalized to settings in which the buyers and sellers themselves have online bidding strategies, rather than just each having individual bids. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2006-09-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 53 Issue Number 5 Page Count 35 Starting Page 845 Ending Page 879

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Source: ACM Digital Library