Vindictive bidding in keyword auctions

We study vindictive bidding, a strategic bidding behavior in keyword auctions where a bidder forces his competitor to pay more without affecting his own payment. We show that most Nash equilibria (NE) are vulnerable to vindictive bidding and are thus unstable. There always exists a pure strategy Nash equilibrium (PSNE) if there is only one pair of vindictive players; however PSNE may not exist when there are at least three players who are all vindictive with each other. Given the set of vindictive bidding pairs, we show how to compute a PSNE if one exists. Preliminary data analysis suggests that vindictive bidding is prevalent in real-world keyword auctions. As an ongoing work, we also propose several interesting open problems related to vindictive bidding.