Capturing the structure of Internet auctions: the ratio of winning bids to the total number of bids

Transcription

1 Capturing the structure of Internet auctions: the ratio of winning bids to the total number of bids Hiromichi Araki and Shigeo Matsubara Department of Social Informatics, Kyoto University, Kyoto Japan Abstract Internet auctions have become popular and have a significant role in the further development of electronic commerce. Capturing the structure of Internet auctions, however, has not been sufficiently attained. An important feature in Internet auction is the existence of micro-macro link. As a first step to analyze micro-macro link we investigate the process from the macro-level phenomena to the micro-level behaviors. We focus on bidders learning ability of the quoting prices and examine the real auction data in a certain period for the identical goods. To enable the analysis, we introduce the ratio of winning bids to the total number of bids (RWT). An interesting feature of RWT is that it pays attention to losing bids as well as winning bids. The results showed that the winners are superior in learning the quoting prices compared to the losers. 1. Introduction Internet auctions have become popular and have a significant role in the further development of electronic commerce. Capturing the structure of Internet auctions, however, has not been sufficiently attained. Analyzing the link structure of web pages has been actively studied. For example, the studies of link structure showed that the degree distribution of incoming links obeys the power law [1] and are utilized to improve the performance of search engines. Compared to web pages, auctions are more dynamic and affected by human behavior. Internet auctions have been actively studied in the various fields such as economics and computer science. An interesting topic is last minute bidding that a non-negligible fraction of bids is submitted in the closing seconds [2]. Another interesting topic is reputations systems to ensure honest behaviors of sellers and buyers [3]. To enable us the further understanding of Internet actions, we try to examine a micro-macro link. As a first step to analyze the micro-macro link in Internet auctions, we investigate the process from the macro-level phenomena to the micro-level behaviors. More specifically, we examine bidders learning abilities and show that the winners are superior in learning the quoting prices compared to the losers. In this analysis we consider auctions in a certain period for the identical goods and introduce the ratio of winning bids to the total number of bids (RWT). An interesting feature of RWT is that it pays attention to losing bids as well as winning bids. The rest of this paper is organized as follows. In section 2, we describe the feature of Internet In section 3, we discuss losing bids in Internet Section 4 defines a quoting price in Internet Section 5 defines RWT and describes the feature of it. In section 6, we show the result of analysis. Finally we conclude this paper in Section The Feature of Internet Auctions In this section, we describe the feature of Internet

2 An important feature in Internet auction is the existence of micro-macro link. As a first step to analyze micro-macro link we investigate the process from the macro-level phenomena to the micro-level behaviors Learning of the quoting price We focus on bidders learning ability of the quoting prices. Comparing the Internet auctions with the general auctions, one of the biggest differences is that spatial goods are sold continuously in Internet Therefore, participants can get the information about the price of the winning bids and the other bids in the auctions for the good they want to get. In other words, they can learn the quoting price in Internet For example, although a participant did not have the information about the quoting price of the good, he /she can bid the proper price by learning the quoting price of the auctions which he/she observed or bided. Therefore, Internet auctions have the feature that bidders can learn the quoting price through the auctions for the good. 3. Losing Bids in Internet Auctions In this section, we describe losing bids in Internet We found an interesting phenomenon that many participants bid the price which cannot be a winning bid in Internet For example, when a good A is always sold at more than 5000 yen in Internet auctions, bidding 3000 yen has no chance to win. Many bidders, however, do such things in Internet In the Internet auction protocols, the last price is defined by the highest bid and the second highest bid. Therefore, the losing bid which is not the second highest bid has no connection with the last price in the auction. However, we consider the losing bid as the important materials in capturing Internet 3.1. Hypotheses about the losing bids Why there are many losing bids which cannot be winning bids in Internet auctions? We form three hypotheses as follows. : Mistake in estimating the quoting price : Bidder s subjective reasons : Shill bidd ing Shill bidding in is the behavior of sellers to enhance their own They bid their own auctions using another IDs. The problem about shill bidding was discussed in the past research [4]. However, in Internet auctions, there are less shill bids than the other losing bids. Therefore, we should discuss and in order to capture the structure of Internet We assume that the reason why such losing bids exist almost include and/or. Bidder s subjective reasons in include the following cases. One example is that a bidder does not want to pay the higher price than his/her subjective price which is less than the minimum winning bid although he/she knows the quoting price. Another example is that a bidder may think that participating or bidding Internet auctions is more significant than winning them. Raveling such bidder s subjective reasons is very difficult only by analyzing the objective data such as bid history. Therefore, this paper particularly considers the mistake in estimating the quoting price in by defining quoting price and RWT Winner and loser We divide participants in the auctions for the spatial good in a certain period into winners and losers. The winner is the participant who won the auction for the good more than once in the period. On the other hand, the loser is the participant who could not win it. Bids by the winners usually include losing bids. Therefore, dividing participants into the winners and the losers enables to analyze the difference of the winners losing bids and the losers ones. In other words, we can examine that the difference of them in learning the quoting prices. 4. Quoting Price In this section, we define a quoting price in Internet We view auctions as follows. A quoting price is

3 formed by bid submissions of bidders and it constrains the behaviors of the bidders. Each bidder thinks he/she do not want to pay the price higher than the quoting price, while different bidders may have different estimate of a quoting price. This paper defines,, a quoting price of auctions for good in the period, as an interval of (,,,,, where, is the average of winning bids in auctions for a good in a period, and, is the standard deviation of winning bids in auctions for the good in the period. 5. The Ratio of Winning Bids to the Total Number of Bids (RWT) 5.1. The definition of RWT In this section, we define the ratio of winning bids to the total number of bids (RWT) and describe the characteristic of RWT. RWT is an index to capture the structure of Internet Auctions. RWT is defined as follows.,,,, where, is the ratio of auctions for a good which were sold at the price less than or equal to in a period,,, is the number of auctions for the good which were sold at the price less than or equal to in the period, and, is the number of auctions for the good which were sold in the period. A characteristic of RWT is that it pays attention to losing bids as well as winning bids. We can deal losing bids relatively according to, which was calculated by winning bids. We consider each bid in auction structure analysis corresponds to each incoming link in the link structure analysis The reason to use RWT One reason why we use RWT when we consider the bidders ability is that we can treat all bids as the common index within 0 to 1 in all goods sold at various price ranges by using RWT. RWT covers all winning bids and we can deal the losing bids as well as winning bids according to,. Another reason is that RWT is the index near to thinking of buyers and sellers. When a bidder estimates the quoting price, he/she cannot know all bids in auctions for the good. Therefore, he/she observes several auctions and tries to bid some of them. Almost bidders do not know the quoting price which we defined in Section 4, but they can know the amounts of winning bids or the other bids in auctions which they observed. Many of them hope to pay the lower prices in winning bids they observed and want to pay not the high price which many auctions were sold at less than or equal to but the lower price at which a few auctions were sold. For example, they want to pay not the price at, 0.9 but the price at, 0.1. On the other hand, when sellers decide the start price, they should consider RWT in order to get more profits. For example, even if the start price is, 0.9, the auction may be sold. Therefore, thinking of buyers and sellers is similar to the RWT s concept and RWT is useful in considering the bidders learning ability. 6. Analysis and Results In this section, we describe the result of analyzing the live data considering RWT Data We used the live data in Yahoo! Auctions Japan 1, the largest Internet auctions site in Japan, and analyzed the bid histories where the each bidders last manual bid amounts are recorded. We set a period at 1st Sep 2008 to 22th Oct In order to capture the feature of a quoting price, we focused attention on two identical goods, a good and a good. The good is a rare CD which is limited-production and sold out in general record stores. It was sold at 112 auctions which includes 491 bids in the period p. The good is a 5,000 yen book token redeemable in participating bookshops in Japan. It was sold at 112 auctions which includes 298 bids in the period p. 1

4 We predict that an identical good has ambiguity in estimating the quoting price. differs in quality and is very difficult to estimate the quoting price. On the other hand, does not differ in quality and is very easy to estimate it Analysis of quoting price We show the result of the analysis about quoting prices. Quoting prices can be calculated as follows:, : ( , ) and, : ( , )., is the higher standard deviation and has the wider interval of the quoting price. On the other hand,, is the smaller and is the good which has the shorter interval of quoting price and has less variation Movement of RWT In Figure 1, we show the movements of, and,., rises from 0 to 1 in a long span. However,, rises in a very short span. These results mean that the degree of ambiguity in is high and the one in is low and estimating the quoting price of is more difficult than Analysis of losing bids We show a result of analyzing the losing bids, which are divided into the winners losing bid and the losers ones, in auctions for and. In auctions for, the number of losing bids by the losers is 332 and one by the winners is 47. In the auctions for, the number of losing bids by the losers is 149 and one by the winners is 49. We classify losing bids into six domains according to the value of, and compare the ratio of the number of them to the total number of losing bids by the winners or the losers. Figure 2 shows the result of the analysis in and Figure 3 shows one in. In these figures, six domains are defined as lows: :, 0, :0,, :,, :,, :, 0.8 and RWTg,p(b) b (yen) g g1 g g2 Figure 1. Moveme nts of, :0.8, 1. First we discuss the losing bids by the losers. In the losers losing bids in auctions for, has the highest ratio of them, followed by,. Especially, more than half of them are included in. Therefore, more than half of the losers bids are less than the minimum price of winning bids and the ratio of them in the domain 0, which includes and is 82% to the total number of losers bids. On the other hand, in the losers bids in auctions for, has the highest ratio of them, followed by,. The ratio of bids in the domain 0, which includes and is 75% to them. In addition, in the auctions for both the good and, the ratio of them in or or are each less than 5% to them. Secondly we discuss the losing bids by the winners. The distribution of them differs from one of the losers bids. In auctions for, each ratio of them are over 15% to the total winners losing bids in,,, and and almost bids are included in these domains. In auctions for, the distribution is closely similar to one of the loser s and the ratio of bids in and is 76% Comparison of the bidders learning ability The above results indicate the following things. Many of the losers bided auctions for at the less price than the minimum winning price where, 0 or the price where, is very low because is difficult to estimate the

5 quoting price. However, many of the winners losing bids are included in the domain where, is higher than loser s major domain. We suppose that the difference between the winners and the losers is caused by mistake in estimating the quoting price. The winners estimate the higher prices and could win by bidding one auction or several However, the losers estimated lower prices than the winners and could not learn the quoting price well. In other words, the winners are superior in learning the quoting prices compared to the losers. On the other hand, is easy to estimate the quoting price. Therefore, almost losing bids are included in and where the prices of bids are lower than, and and have the capability to be winning bids. These results show that the losers and winners estimated the similar quoting prices in auctions for the good. The difference in the learning ability between the winners and the losers in auctions for which is easy to estimate the quoting price is smaller than which is difficult to do. 7. Conclusions In this paper, in order to analyze micro-macro link, we investigated the process from the macro-level phenomena to the micro-level behaviors. Particularly, we focused on bidders learning ability of the quoting prices and examine the real auction data in a certain period for the identical goods. We introduced the ratio of winning bids to the total number of bids (RWT) in order to enable the analysis. A characteristic of RWT is paying attention to not only winning bids but also losing bids. We can analyze the losing bids with the common index RWT and can know easily the ratio of losing bids in the spatial domain classified by the value of RWT in spite of the difference of the prices. In Internet auctions, there are many losing bids whose prices are very lower than minimum winning bids. We proposed the three hypotheses of existing of them. Particularly, we consider mistake in estimating the quoting price using RWT. The results Ratio of losing bids Ratio of losing bids 0.0 D0 D1 D2 D3 D4 D5 Domain Loser Winner Figure 2. Ratio of losing bids ) 0.0 D0 D1 D2 D3 D4 D5 Domain Loser Winner Figure 3. Ratio of losing bids ) showed that the winners are superior in learning the quoting prices compared to the losers. Acknowledgment This research was supported by a Grant-in-Aid for Scientific Research (B) ( , ) from Japan Society for the Promotion of Science (JSPS). References [1] R. Albert, H. Jeong and A. L. Barabasi. Diameter of the world-wide web, Nature, Vol. 401, pp , [2] A. Ockenfels and A. E. Roth. Last Minute Bidding and the Rules for Ending Second- Price Auctions: Evidence from Ebay and Amazon Auctions on the Internet, American Economic Review, 92(4), pp , [3] D. Houser and J. C. Wooders. Reputation in Auctions: Theory, and Evidence from ebay, Journal of Economics & Management Strategy, Vol. 15, pp , [4] I. Chakraborty and G. Kosmopoulou. Auctions with shill bidding, Economic Theory, Vol.24, No.2, pp , 2004.