An auction model with reserve price and commission rate in the form of a quadratic function

This paper investigates a sealed-bid auction model including a quadratic function form of the commission rate. Firstly, we provide the equilibrium bidding strategies for both first-price and second-price sealed-bid auctions. Secondly, we obtain the expected revenue of bidders and sellers for the two auction modes. Finally, we study the influence of the reserve price and the coefficient in the commission rate on the equilibrium bidding strategy, and the expected revenues of the bidder and the seller. The results indicate that the commission rate coefficient and reserve price have the same impact on the equilibrium bidding strategy and seller's expected revenue. Bidders are more willing to choose a first-price auction because their expected revenue is greater than that in a second-price auction. The commission rate in the form of a quadratic function proposed in this paper not only meets the requirements of real auctions but also has theoretical research value.