Algorithms for maximum social welfare of online random trading

Abstract

In an online random trading problem, m sellers and n buyers arrive in a random sequential order to meet a decision maker. Each seller possesses an item and each buyer demands an item. All items are identical. Each agent (seller or buyer) has a positive valuation on one item and reveals her valuation to the decision maker when she arrives. The decision maker, who knows only m and n in advance, uses an online algorithm to make an irrevocable decision on whether or not to trade with the arriving agent at her arrival time. We design online algorithms to maximize the social welfare, i.e., the expected total valuation of the agents who possess items on hand at the end of trading process. For the single-buyer trading, our algorithm achieves a tight competitive ratio of 1+1/m. For the single-seller trading, when n tends to infinity, we establish lower bound 3.258 and upper bound 4.189 on the competitive ratio. When both m and n are sufficiently large, our algorithm achieves an asymptotic competitive ratio no more than 1+O(m−1/3lnm).