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 {\em 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 $v_iq_j$. We want to decide the allocations and the prices in order to maximize the total revenue of the market maker. A key difference from the traditional position auction is the advertiser's requirement of a fixed number of consecutive slots. Consecutive slots may be needed for a large size rich media ad. We study three major pricing mechanisms, the Bayesian pricing model, the maximum revenue market equilibrium model and an envy-free solution model. Under the Bayesian model, we design a polynomial time computable truthful mechanism which is optimum in revenue. For the market equilibrium paradigm, we find a polynomial time algorithm to obtain the maximum revenue market equilibrium solution. In envy-free settings, an optimal solution is presented when the buyers have the same demand for the number of consecutive slots. We conduct a simulation that compares the revenues from the above schemes and gives convincing results.Comment: 27page

On Revenue Maximization with Sharp Multi-Unit Demands

We consider markets consisting of a set of indivisible items, and buyers that have {\em sharp} multi-unit demand. This means that each buyer $i$ wants a specific number $d_i$ of items; a bundle of size less than $d_i$ has no value, while a bundle of size greater than $d_i$ is worth no more than the most valued $d_i$ items (valuations being additive). We consider the objective of setting prices and allocations in order to maximize the total revenue of the market maker. The pricing problem with sharp multi-unit demand buyers has a number of properties that the unit-demand model does not possess, and is an important question in algorithmic pricing. We consider the problem of computing a revenue maximizing solution for two solution concepts: competitive equilibrium and envy-free pricing. For unrestricted valuations, these problems are NP-complete; we focus on a realistic special case of "correlated values" where each buyer $i$ has a valuation v_i\qual_j for item $j$, where $v_i$ and \qual_j are positive quantities associated with buyer $i$ and item $j$ respectively. We present a polynomial time algorithm to solve the revenue-maximizing competitive equilibrium problem. For envy-free pricing, if the demand of each buyer is bounded by a constant, a revenue maximizing solution can be found efficiently; the general demand case is shown to be NP-hard.Comment: page2

Pricing ad slots with consecutive multi-unit demand

We consider the optimal pricing problem for a model of the rich media advertisement market, that has other related applications. Our model differs from traditional position auctions in that we consider buyers whose demand might be multiple consecutive slots, which is motivated by modeling buyers who may require these to display a large size ad. We study three major pricing mechanisms, the Bayesian pricing model, the maximum revenue market equilibrium model and an envy-free solution model. Under the Bayesian model, we design a polynomial-time computable truthful mechanism that optimizes the revenue. For the market equilibrium paradigm, we find a polynomial-time algorithm to obtain the maximum revenue market equilibrium solution. In the envy-free setting, an optimal solution is presented for the case where the buyers have the same demand for the number of consecutive slots. We present results of a simulation that compares the revenues from the above schemes

Pricing ad slots with consecutive multi-unit demand

We consider the optimal pricing problem for a model of the rich media advertisement market, that has other related applications. Our model differs from traditional position auctions in that we consider buyers whose demand might be multiple consecutive slots, which is motivated by modeling buyers who may require these to display a large size ad. We study three major pricing mechanisms, the Bayesian pricing model, the maximum revenue market equilibrium model and an envy-free solution model. Under the Bayesian model, we design a polynomial-time computable truthful mechanism that optimizes the revenue. For the market equilibrium paradigm, we find a polynomial-time algorithm to obtain the maximum revenue market equilibrium solution. In the envy-free setting, an optimal solution is presented for the case where the buyers have the same demand for the number of consecutive slots. We present results of a simulation that compares the revenues from the above schemes

Pricing ad slots with consecutive multi-unit demand

We consider the optimal pricing problem for a model of the rich media advertisement market, that has other related applications. Our model differs from traditional position auctions in that we consider buyers whose demand might be multiple consecutive slots, which is motivated by modeling buyers who may require these to display a large size ad. We study three major pricing mechanisms, the Bayesian pricing model, the maximum revenue market equilibrium model and an envy-free solution model. Under the Bayesian model, we design a polynomial-time computable truthful mechanism that optimizes the revenue. For the market equilibrium paradigm, we find a polynomial-time algorithm to obtain the maximum revenue market equilibrium solution. In the envy-free setting, an optimal solution is presented for the case where the buyers have the same demand for the number of consecutive slots. We present results of a simulation that compares the revenues from the above schemes