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Mathematical Problems in Engineering
Volume 2015, Article ID 301734, 9 pages
Research Article

Bayes-Nash Equilibrium of the Generalized First-Price Auction

1School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China
2Hebei Academy of Governance, Shijiazhuang 050031, China

Received 9 June 2015; Revised 19 September 2015; Accepted 21 September 2015

Academic Editor: Anna M. Gil-Lafuente

Copyright © 2015 Xiaohu Han and Shulin Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analyze the generalized first-price auction under incomplete information setting. Without setting a reserve price, the efficient symmetrical Bayes-Nash equilibrium is characterized and found to be increasing as the number of bidders is sufficiently large. Then, the explicit expression for the expected revenue of the search engine is found and the effect of the click rates of all the positions on the expected revenue is obtained. Finally, with setting of the reserve price, we have found the optimal reserve price and examine how the difference of the search engine’s revenues with setting reserve price and without setting reserve price varies with the reserve price.