Pricing ad slots with consecutive multi-unit demand

We consider the optimal pricing problem for a model of the rich media advertisement market, as well as other related applications. In this market, there are multiple buyers (advertisers), and items (slots) that are arranged in a line such as a banner on a website. Each buyer desires a particular number of consecutive slots and has a per-unit-quality value v i (dependent on the ad only) while each slot j has a quality q j (dependent on the position only such as click-through rate in position auctions). Hence, the valuation of the buyer i for item j is v i q j . We want to decide the allocations and the prices in order to maximize the total revenue of the market maker.