Competitive Safety Strategies in Position Auctions

Abstract

We attempt to address the challenge of suggesting a useful bidding strategy to an agent in the an ad auction setting. We explore the possibility of using competitive safety strategies in that context; a C-competitive strategy guarantees a payoff which is no less than 1/C of the payoff obtained in a best Nash equilibrium. We adopt the model of ad auctions suggested by Varian and provide analysis of competitive safety strategies in that context. We first show that no useful safety competitive strategies exist in a setting with complete information about the agents’ valuations. Namely, in a setting with N bidders and exponential click-rate functions the ratio can be arbitrarily close to N. We also show that N is a general upper bound for any click-rates and valuations, while $\sum_{t=1}^N \frac{1}{t}$ is a tight bound for linear click-rates. However, in our main results we show that, surprisingly, useful C-competitive strategies do exist in the incomplete information setting. More specifically, we show that under the assumption that agents’ valuations are uniformly distributed, an e-competitive strategy exists for the case of exponential click-rate functions, and a 2-competitive safety strategy exists for linear click-rate functions.