Forward looking Nash equilibrium for keyword auction

We introduce the concept of forward looking Nash equilibrium for the position auction (also called the generalized second price auction), a widely studied protocol for Internet advertisement bidding processes. We show that it has a unique solution for the position auction. Most importantly, the cost each bidder pays and the revenue of the auctioneer under the equilibrium are all equal to those under VCG mechanism. As the position auction is not an incentive compatible protocol, the fact that the forward looking Nash equilibrium results in the same payoff for everyone as in the VCG protocol justifies the practical protocol.