On the theory of truthful and fair pricing for banner advertisements

We consider revenue maximization problem in banner advertisements under two fundamental concepts: Envy-freeness and truthfulness. Envy-freeness captures fairness requirement among buyers while truthfulness gives buyers the incentive to announce truthful private bids. A extension of envy-freeness named competitive equilibrium, which requires both envy-freeness and market clearance conditions, is also investigated. For truthfulness also called incentive compatible, we adapt Bayesian settings, where each buyer's private value is drawn independently from publicly known distributions. Therefore, the truthfulness we adopt is Bayesian incentive compatible mechanisms. Most of our results are positive. We study various settings of revenue maximizing problem e.g. competitive equilibrium and envy-free solution in relaxed demand, sharp demand and consecutive demand case; Bayesian incentive compatible mechanism in relaxed demand, sharp demand, budget constraints and consecutive demand cases. Our approach allows us to argue that these simple mechanisms give optimal or approximate-optimal revenue guarantee in a very robust manner