Design of optimal auction for online commerce

Optimal design of auction is one of hot research topics in the auction theory. Regarding starting the price as decision variable, here we study the optimal design of online auctions, by considering some features of online auctions, the stochastic entry of bidders (subject to Poisson process), the insertion fee proportional to the starting price, commission rates, buy-in penalties and time discount. We have analyzed the properties of extremum points of the starting price for maximizing seller's expected revenue, and found that, under certain conditions, the optimal starting 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 in which the seller, auction site and a total of two achieve simultaneously their own maximum, and the relations between starting price and some parameters. At last, some directions for further research are also put forward.