Online algorithms for market clearing

13 years 4 months ago

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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 profit, we present a (randomized) online algorithm with a competitive ratio of ln(pmax - pmin)+1, when bids are in a range [pmin, pmax], 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 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 subsidize matches--match money-losing pairs if it has already collected enough money from previous pairs to pay for them--then it can ...

Avrim Blum, Tuomas Sandholm, Martin Zinkevich

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