In this dissertation, I model generalized second price (GSP) auction for keyword search to analyze the optimal bidding strategies of the participating advertisers. The results also apply to a more general setting where multiple goods are being auctioned off. The study in chapter 3 examines the bidding strategies of the advertisers in a complete information static GSP auction. The results show that unlike in standard second price auction, truthful bidding is never a dominant strategy in general second price auction. In chapter 4, I have developed a model of static incomplete information GSP auction. I characterize all possible pure strategy Bayes-Nash equilibrium of the game and show that the consideration of the click through rates ratio plays a key role in determining the equilibrium bidding strategies for the advertisers. Specifically, I find that when the click through rates ratio exceeds a critical value, there will be no pure strategy Bayes-Nash equilibrium. The analysis also reveals that in a game of static incomplete information no asymmetric bidding equilibrium would prevail. The study in chapter 5 analyzes a model of incomplete information dynamic GSP auction. I find that in a dynamic game, the existence of both separating strategy equilibrium and pooling strategy equilibrium would depend upon critical values of click through rates ratio. I also prove that the advertisers with high valuation for a keyword will either reveal their identities at the very beginning or at the very end of this dynamic game. The results also show that when search engines do not publish the bidding history (i.e. there is 'minimum disclosure of information'), the advertisers will never try to mimic each other or in other words, there will be no pooling strategy equilibrium.