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. Pure strategy Nash equilibria (PSNE) may not exist when there are at least three players who are all vindictive with each other. And there always exists a PSNE if there is only one pair of vindictive players. Given the set of vindictive bidding pairs, we show how to compute a pure strategy Nash equilibrium (if one exists). As an ongoing work, we also propose several interesting open problems related to vindictive bidding.
Yunhong Zhou, Rajan M. Lukose