Game theoretical analysis of buy-it-now price auctions

We study two kinds of buy-it-now options, temporary and permanent, under a theoretical model of Stackelberg game. In this two-stage game, the bidders, as the followers, use a two-threshold strategy to determine whether to bid or directly buy the item at the posted price, given an auction configuration featured by the seller in the first stage and other common knowledge. Under the uniform distribution assumption for the bidders' valuation, we derive the optimal necessary conditions of the starting price and the buy-it-now price for maximizing the seller's expected revenue. Then, we use two numerical experiments to find some interesting insights, which include that under identical bidders' participation costs, the temporary buy-it-now option can acquire a higher expected revenue for the seller than the permanent option, and a buy-it-now price auction always nontrivially dominates a regular auction in terms of the achieved expected revenue, no matter whether the seller or the bidders are risk-averse.