Sponsored search has become a principal source of revenue for search engine companies. The business model relies on advertisement sales that provide advertisers opportunities to introduce their products directly to potential customers. Pricing of such advertising positions has been vitally important for the search engines. The generalized second price auction has turned out to be the primary protocol for such sponsored search markets.

While several Nash equilibria may exist for the generalized second price auction, we propose the concept of the forward looking Nash equilibrium as the bidder's individual rational manipulation outcome. We further identify and focus on traffic arbitrage and click arbitrage possibilities crossing multiple markets as well as derive and characterize equilibria across markets