Bid pricing in online auctions with "Buy-It-Now" option

The present note suggests a decision theoretic and practical rule for auctioneers to set out prices in online auctions in presence of Buy-It-Now options. The minimum starting bid and the Buy-It-Now price are calculated as an intuitive function of seller’s evaluation of the final price stochastic distribution and of seller’s attitude toward the price variability. Specifically, the presence of personalized parameters permits to incorporate the seller pessimism in stating the starting minimum bid and the seller optimism in fixing the Buy-It-Now price. The pricing rule is based on the Extended Gini premium principle, a well-known premium principle in non-life insurance literature that has been recently proposed in different areas of finance and portfolio risk management. In addition to give closed-end formulae for the starting minimum bid and Buy-It-Now price, we provide numerical tables for a number of common distributions for the ending price at different levels of seller’s risk-aversion and gain-propensity. Discussion on the spread between the starting minimum bid and Buy-It-Now price is also carried out.