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A Risk-Free Refinement of Symmetric Nash Equilibrium in Generalized Second-Price Keyword Auctions

Symmetric Nash equilibrium is a well-known refinement of Nash equilibrium in the study of bidding behavior of online advertisers on the sponsored search advertising marketplace. This solution concept, however, has major limitations. It allows for over-bidding and has uncompelling upper bounds. In this paper, we propose a risk-free refinement of symmetric Nash equilibrium (RfSNE), to tackle these limitations. RfSNE can be determined by a bottom-up recursive algorithm. At an RfSNE, no advertiser is exposed to the risk of payoff loss caused by over-bidding. Managerially, RfSNE can be employed by search engines to help advertisers plan bidding strategy and the revenues realized on the set of RfSNEs can be used as a benchmark to evaluate alternative auction mechanisms.