Characterizing Optimal Keyword Auctions ∗

We present a variety of models for keyword auctions used for pricing advertising slots on the search engines (Google Inc., Yahoo! Inc. etc.). First, we formulate the general problem that allows the privately known valuation per click to depend both on the identity of merchant and the slot and presents a compact characterization of the set of all deterministic incentive compatible direct mechanisms. In particular, we show that there are incentive compatible mechanisms which are not affine maximizers in this multidimensional type model. Next, we study two interesting cases of this model: slot independent valuation and privately known constant valuations (i.e. slot independent) up to a privately known slot and zero thereafter. We characterize revenue maximizing as well as efficiency maximizing incentive compatible (IC) and individually rational (IR) mechanisms. These mechanism are computationally efficient with time complexity O(nm) where n is no. of bidders and m is no. of slots. We also characterize the optimal mechanism when the mechanism is restricted to be rank-based. We use dominant strategy equilibrium as the solution concept.