Learning Unknown Private Valuation in Generalized Second Price Position Auction

Many studies have focused on the generalized second price (GSP) auction under uncertainty, particularly with unknown private valuation, Bayesian-Nash equilibrium, social welfare loss and reserve price. However, the learning path for players in the GSP auction remains inadequately addressed. As a sequential and repeated auction with a large number of players, the process of removing uncertainty in the GSP auction is similar to social observational learning, where information aggregation and herding play a crucial role. Furthermore, as the number of players increases, mean field game theory suggests that players’ beliefs will converge to their expected value. In this paper, we propose a comprehensive cognitive framework that shows how players form and update their beliefs through collective learning. We present a mathematical model that provides detailed quantitative analysis and confirms that the hypothetical learning process leads to the convergence of beliefs or expected valuations. Simulation experiments further support our conclusion