On the robustness of forward looking nash equilibrium in sponsored search auction

Abstract

Internet advertising has become one of the most popular advertising norm for most big and small companies. Companies motivated by Search Engine technologies such as Yahoo, Google, Baidu make billions of dollars in revenue by selling advertisements with auction mechansim. The corresponding mechanism, known as sponsored search auction, is best modelled as Generalized Second Price (GSP) Auction and has been intensively studied. Variants studied the protocol in terms of its equilibrium solutions with focus on a subset - Symmetric Nash equilibrium while Edelman et al. investigated a concept called Local Envy Free and the corresponding equilibrium solution - Local Envy Free Equilibrium. According to their works, GSP was not incentive compatible where no advertiser can maximize his by telling his true value. On the other hand, their works also the usage of GSP as the protocol to sell advertisements. They all derived equilibrium solutions whose revenues are at least as high as the VCG mechanism. Bu et al. further studied bidding dynamics of protocol. They proposed a bidding strategy motivated by an attribute of looking one step further called Forward Looking strategy which resulted in a unique Nash equilibrium point same as the one under VCG mechanism. In particular, Bu et al. substantiated the convergence property of their strategy under randomized dynamics process. Cary et al., meanwhile, studied the dynamics with the greedy rationality. However, all their works rely on cooperation that all of the participants implements the same strategy, where competitors' strategic behaviors might not be the case in the real world. In this thesis, I study the robustness of forward looking attribute against other bidding rationalities. I focus on an aggressive strategic heuristic, called vindictive bidding. I investigate three types of such bidding strategies. I substantiate that forward looking strategy is robust against such vindictive strategy that pure Nash equilibrium still exists under two of the strategies even if there is arbitrary portion of vindictive bidders. To further justify forward looking as a suitable bidding strategy, I study the bidder incentive in the dynamic process. Empirical evidence is given to show that forward looking is better against vindictive strategy in most cases. When a user migrates from forward looking strategy to any of the vindictive strategy. His utility is most likely to decrease. With the growth of the number of vindictive bidders, the auctioneer's revenue keeps increasing. Especially, when all the bidders take the selective vindictive strategy, the auction reaches a Nash equilibrium with the maximum revenue, which is worst to all the bidders. Thus we conclude that bidders do not have much incentive to use any of the vindictive strategies.