On Robustness of Forward-looking in Sponsored Search Auction

We analyze the robustness of pure Nash Equilibria of sponsored search auctions, based on the forward-looking response function. To consider the robustness of such refined solution concept, we first study the convergence property of several adjustment schemes. Especially, we prove that under the randomized scheme, the auction always converges to a unique fixed point with probability one, whose revenue is equal to the celebrated VCG mechanism. Additionally, we study the robustness of such forward-looking strategic heuristic against aggressive selfish strategic heuristic called vindictive bidding. We investigate three types of such bidding strategies and substantiate that the pure Nash equilibrium still exists under two types even if there is an arbitrary portion of vindictive bidders.