Online Ad Assignment with an Ad Exchange

Ad exchanges are becoming an increasingly popular way to sell advertisement slots on the internet. An ad exchange is basically a spot market for ad impressions. A publisher who has already signed contracts reserving advertisement impressions on his pages can choose between assigning a new ad impression for a new page view to a contracted advertiser or to sell it at an ad exchange. This leads to an online revenue maximization problem for the publisher. Given a new impression to sell decide whether (a) to assign it to a contracted advertiser and if so to which one or (b) to sell it at the ad exchange and if so at which reserve price. We make no assumptions about the distribution of the advertiser valuations that participate in the ad exchange and show that there exists a simple primal-dual based online algorithm, whose lower bound for the revenue converges to $R_{ADX} + R_A (1 - 1/e)$, where $R_{ADX}$ is the revenue that the optimum algorithm achieves from the ad exchange and $R_A$ is the revenue that the optimum algorithm achieves from the contracted advertisers.