The generalized second price auction has recently become a much studied model for sponsored keyword auctions for Internet advertisement. Though it is known-not to be incentive compatible, properties of its pure Nash equilibria have been well characterized under the single bidding strategy of each bidder. In this paper, we study the properties of pure Nash equilibria of the generalized second price auction when each bidder is allowed to submit more than one bid. This multi-bidding strategy is noted to have been adopted by companies for keyword advertisements on search engines. In consideration of the pure Nash equilibria, we completely characterize conditions on the number of selling slots for a pure Nash equilibrium to exist, assuming all the advertisers are allowed to use multi-bidding strategies or only one advertiser will use a multi-bidding strategy. Our findings reveal interesting properties of limitation and potentials of the market place of online advertisement.
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