Correcting vindictive bidding behaviors in sponsored search auctions

In this study, we aim to develop a pricing mechanism that reduces the effects resulted by vindictive advertisers who bid on sponsored search auctions run by search engine providers. In particular, we aim to ensure payment fairness and price stability in these auctions. With the generalized second price principle, advertisers pay the next-ranked bid value rather than the price that they bid. Vindictive bidders take advantage of this principle to manipulate the payment of a previously-ranked advertiser. Vindictive bidding results in unfair outcomes and eliminates equilibria. However, it is difficult to compute rational payments for all advertisers as advertisers’ valuations are private. Our proposed mechanism decreases the payment to make up for the utility loss that is induced by vindictive bidding. The vindictive advertiser is simultaneously punished with an additional payment. According to our theoretical analyses and simulations, the proposed mechanism efficiently decreases the effects that result from vindictive bidding, and guarantees equilibrium outcomes.