Willingness to spend (WTS), as defined by the amount a bidder is willing to spend in a particular auction event, is a crucial component for an auction's success. This paper investigates the dynamics of WTS of a simultaneous online auction of a specific genre of fine art called modern Indian art and compare it with the dynamics of cumulative Willingness to pay (WTP), using an innovative statistical method called Functional Data Analysis. Functional Data Analysis, which is fundamentally considered to recover the underlying WTS and cumulative WTP function curves of each bidder, is further used to examine the effects of current number of bids, current number of lots winning, pre-auction low estimate of the lots they are currently winning, bid time, and number of proxy bids on WTS and cumulative WTP dynamics. Results suggest that only current number of bids and bid time have significant positive effect on the bidder WTS, whereas only current number of bids have influence on cumulative WTP. Implications for auction house managers are further discussed in the paper.
Keywords: willingness to spend, functional data analysis, dynamic modeling, simultaneous online auctions, online fine art auctions
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With the growing popularity of online auctions and easy availability of detailed bidding information, we now have a greater prospect in micro-analyzing various online auction bidding behaviors in different auction settings that were not possible earlier. To a greater extent, we have capitalized on this opportunity by addressing a wide range of online auction topics, including, for example, auction formats [Jap 2002; Jap 2003; Lucking-Reiley 1999; Spann and Tellis 2006], price dynamics and forecasting [Jank and Shmueli 2006; Reddy and Dass 2006; Dass, Jank and Shmueli 2010], bidders' willingness to pay [Park and Bradlow 2005; Chan, Kadiyali and Park 2007], reference points [Dholakia and Simonson 2005; Kamins, Drenze and Folkes 2004], buyer and seller reputation [Melnik and Alm 2002], herding behavior [Dholakia, Basuroy and Soltysinski 2002], forward-looking behavior [Zeithammer 2006], bidder experience [Borle, Boatwright and Kadane 2006], bidder heterogeneity and auction design [Bapna et al. 2004]. Although these studies have expanded our understanding of online auctions, other bidder behavioral phenomena are still not examined. One such topic is bidders' willingness to spend in a simultaneous online auction.
Most of the prior researches in auctions examining bidders' purchase decision and values have focused on their willingness to pay (WTP). These studies investigated what drives bidders' WTP [Noussair, Robin and Ruffieux 2004; Chan, Kadiyali and Park 2007] and how it is different from bidders' willingness to accept (WTA) [Shogren et al. 1994; Plott and Zeiler 2005]. Interestingly, most of these studies assume that bidders are involved in purchasing only one product at a time in the auction. This assumption is not sufficient while examining bidders' purchase decisions in simultaneous online auctions where bidders typically tend to purchase more than one item simultaneously. In such cases, Willingness to Spend (WTS) is the most appropriate bidder metric to consider while examining success of auction houses. From the extant literature, we find examination of WTS mostly in the context of multi-product bundles [Gaeth et al. 2004]. We adopt their definition and define WTS in the context of online auctions as the amount a bidder is willing to spend in a particular auction event. In this paper, we define WTS as the total amount a bidder is required to pay at a given time period during the auction if he/ she wins all the items at the current highest bid amount where he/ she is currently the highest bidder. Therefore, by the above definition, WTS is the superset of Willingness to Pay (WTP) of bidders for the items they wish to purchase, as it is the sum of the WTP of all items. …