Learning unknown private valuation in Generalized Second Price position auction

Abstract

Classical equilibrium analysis of the Generalized Second Price (GSP) auction assumes that all players have complete information—a fundamental premise for theoretical development but one that may not align with real-world scenarios. This discrepancy raises concerns about the applicability of such analyses and has motivated researchers to explore equilibrium behavior under incomplete information. Over the past decade, increasing attention has been given to GSP auctions under uncertainty, particularly in areas such as unknown private valuations, Bayesian-Nash equilibrium, social welfare loss, and reserve pricing. However, the learning dynamics of players in the GSP auction remain largely unexplored.

In this paper, we propose a comprehensive cognitive framework to illustrate how players form and update their beliefs through collective learning. We show that, as a sequential and repeated auction involving numerous participants, the GSP auction’s uncertainty-reduction process closely resembles social observational learning, where information aggregation and herding play critical roles. Furthermore, insights from mean field game theory suggest that players’ beliefs converge to their expected values over time. Our quantitative analysis confirms that this learning process drives belief convergence, while simulation experiments validate the effectiveness of our proposed framework.