Abstract
This paper investigates the revenue and duration of a well-known hybrid oral auction (English auction and Dutch auction) that is extensively adopted in practice, for instance the Christie’s. Unlike sealed bid auction, oral auction is featured by its complexity of dynamic process. The bidding price varies as a stochastic time series. Therefore, the duration of oral auction as well as its revenue performs randomly. From the seller’s perspective, both the revenue and the duration are so important that extra attention and effort should be put on auction design. One of the most important issues is how to choose the starting bid price to maximize its revenue or minimize its duration. In this paper, the bidding process is decomposed into two phases: English auction (descending-bid) phase and the Dutch auction (ascending-bid) phase. For each phase, with the aid of Markov method, we derive the expected revenue and duration as a function of the starting bid. For an oral auction with a large number of bidder and each bidder behaves independently, we provide the limit results of the expected revenue and duration. The results of the auction model can be easily implemented in auction design.
Highlights
As a powerful and well-known tool in business markets, auction plays an important role in selling objects especially for antiques and art
This paper investigates the revenue and duration of a well-known hybrid oral auction (English auction and Dutch auction) that is extensively adopted in practice, for instance the Christie’s
For an oral auction with a large number of bidder and each bidder behaves independently, we provide the limit results of the expected revenue and duration
Summary
As a powerful and well-known tool in business markets, auction plays an important role in selling objects especially for antiques and art. A. Segev, et al model an online auction in terms of a Markov process on a state space defined by the current price of the auctioned item and the number of bidders that were previously “bumped” [12]. Et al model an online auction in terms of a Markov process on a state space defined by the current price of the auctioned item and the number of bidders that were previously “bumped” [12] They first convert an online auction into a small-to-medium sized auction. It is of our interest to derive the expected revenue and duration as a function of the starting bid To this end, we shall first formulate an oral auction model based on Markovian property.
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