Abstract: The seller's strategies of the on-line auction problem are studied in this paper. Traditional assumption that sellers are always risk averse is extended and a risk reward framework is established based on risk preference. Two auction strategies of RPS and MPS are designed for the risk taking sellers. The analyses show that the competitive ratios of these two strategies are lower than one of the traditional strategy, and they can achieve better performance. It proves that the risk preference and forecasts determine the auction quantities and auction prices. Finally, numerical examples show that risk tolerance and auction reward are positive. Furthermore, multiple forecasts on reference prices can improve the sellers' forecasting ability and increase auction reward.

Key words: on-line auction, competitive ratio, risk, reward