Optimal Design of Online Auction with Seller Entry Fee, Buy-In Penalties and Commissions

Optimal design of auction is one of hot research topics in the auction theory. In this paper, we design this online auction mechanism, by considering simultaneously the bidders´ stochastic arrival process, entry fee, which is proportional to the reserve price seller, commission rates, which is proportional to the ultimate winning price from the seller if the item is auctioned off successfully, buy-in penalties from seller if the item is not auctioned off successfully and time discount. We have analyzed the properties of extremum points of the reserve price for maximizing seller´s ,auction site´s and total expected revenue, and found that, under certain conditions, the optimal reserve price should be at the lowest allowable level, which is contrary to results from the classic auction theory and finds its optimality in reality. In addition, we have discussed the condition on which the seller, auction site and total parties achieve simultaneously their own maximum .We also design the optimal combination of buy-in penalties from seller and entry fee and give a numerical analysis. At last, some directions for further research are also put forward.