Performance analysis of sequential Internet auction systems comparing with fixed price case

In this paper, we first present a new performance model and an analysis for its optimal allocation in a sequential Internet auction system with a fixed reserve price. In such a system, a seller wants to sell a given amount of items through sequential auctions on the Internet. The seller has a reserve price for each item. For each auction, the seller should allocate a quantity of items from the total available items to be auctioned. The buyers arrive according to a Poisson process and bid honestly (without collusion, etc.). We consider the sequential Internet auction model to be a Markov decision process and present its performance analysis for the Internet auction model. In the analysis, we show that the result is no difference whether the reserve price is private (known only to the seller) or public (posted on the web). Then we show that in the monotonous properties of the optimal policy, the more items are in hand or the less the horizons remain, the more items are allocated for auction. Next, we compare this auction mechanism with mechanisms of fixed price, dynamic price and sequential auction with dynamic reserve price, respectively, for the seller´s profit and show that the seller will receive more in the auction case than in the price case and more in the dynamic case than in the fixed price case, respectively. Finally, numerical results are given, where we compute the maximal expected total revenue and the solution of the optimal allocation, display the effect of the arrival rate, and discuss the optimal reserve price and the available number of auctions.