A probability distribution for the number of bids in an auction where the prices only drop

Abstract

In an auction website an item was entered for sale with an initial price equal to the market value, the person interested in buying the item could only see it but not its price when accessing the auction. After paying the website $1, the price was automatically reduced by 0.5 dollars and the current price was shown to the bidder. After two minutes, the price was hidden again and the item was relisted. Therefore, the more viewings, the more the item’s price dropped, until someone finally made the purchase. We proposed a probability model for the ‘number of bids required for an item to be sold’, in which the probability of success at each bid is not constant. Named Alê’s distribution after the student who first considered the problem, this model was fitted to auction data and compared with the geometric distribution. A contrasting example from a different context and a simulation study were also conducted to assess performance in various scenarios. The results show that Alê’s distribution can be reliably estimated, correctly identified, and provides a more flexible and accurate model for this type of auction. Estimates of expected gain based on Alê’s distribution are more precise, reflecting its superior fit to the data.

Keywords

• Average profit
• geometric distribution
• non-constant probability.

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