Two mechanisms to overcome the winner’s curse—tested online
Shihan Wu 11585560
Economics: Behavioral economics and game theory
Abstract
I present results from first-price common value auction experiments under two mechanisms to show whether the winner’s curse can be mitigated under the two mechanisms. One mechanism is called sequential order mechanism which is based on anchoring effect and signals are ordered by either descending or ascending true values’ sequence. The other mechanism is called cheap talk mechanism which is the aim of reminding subjects about the existence of the winner’s curse. I found bids in cheap talk script’s treatment is significantly smaller compared to the treatment without cheap talk script. For sequential order mechanism, there is no significant difference between different treatments.
Statement of Originality
This document is written by Student Shihan Wu who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no
sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of
1 Introduction
The winner’s curse, a phenomenon that occurs in common value auction and it depicts a situation under which in order to obtain an item, winners are likely to bid higher than the value of the item in an auction due to emotion or incomplete information. Winner’s curse has been universally observed in people with different experience levels as well as across many types of markets. Thaler (1988) found that it is hard to avoid winner’s curse even for people who have already recognized that the existence of “winner’s curse” phenomenon and have learned a lot about economics. Douglas Dyer (1989) found that inexperienced bidders were observed to overbid in a large market as well as in the small market. What effects make a difference on winner’s curse magnitude also have widely been discussed by many researchers. In light of Neugebauer and et al. (2004) article, overbidding can be influenced by the
different degree of information revelation and will be fostered if bidders only know winning bids after every auction. Kagel (1995) pointed out that bidders intend to bid more with more rivals, which is contradictory to the Nash bidding theory. As for the reason why winner’s curse happens, there are several explanations developed by researchers. For instance, “joy of winning” came up by Cox et al. (1992) is one of the famous explanations.
In common value auction’s setting, the value of an object is identical for all the bidders, but the bidders do not know the exact value of the item and they need to bid for items depending on their obtained information. Bidders will have their own information and the private information is called “signal” in common value auction setting. The signal can be different from person to person, while the true value of the item should be the same for everyone. The real-life example for common value auction can be oil lease auction, famous painting auction, classic a jar of quarters auction, etc.
There is a famous story about winner’s curse. There are several oil companies who are going to contend for a drilling rights on an uncharted land and we assume that an efficient market for oil and technology is available. The value of the right should be identical for each bidder and all bidders make an unbiased estimation of the right according to their private
information. The bids which made by oil companies can constitute a monotone increasing array and the oil company who wins the right tends to have the most optimistic estimation of the right’s value. As a result, the winner is likely to make below normal or even negative
profits and the market is not efficient. Designing economic auction mechanisms can be the approach to solve “winner’s curse”. Instead of putting efforts on changing their behaviors by themselves, bidders’ behaviors can be modified by new auction mechanism. In another word, the magnitude of “winner’s curse” effects may decrease under new auction mechanisms. Two different auction mechanisms are designed to test whether both mechanisms
significantly influence bidders’ bidding behavior. The bidding behavior can be affected by emotion and in this case, designing an economic auction mechanism may modify bidders’ behavior without the need of controlling the bidders’ own emotion. For one auction
mechanism, I add notification before every auction to remind bidders of what “winner’s curse” is and why it happens. This kind of notification can also be called cheap talk script”
according to Ronald G. Cummings and Laura O. Taylor (1999)’s article. In the following sections, this auction mechanism will be called cheap talk mechanism. For the other auction mechanism, signals’ order is based on their corresponding items’ true value sequence which is sorted in either ascending order or descending order. This auction mechanism will be called as a sequential order mechanism in following sections. I set up auction mechanisms to find out if those modified auction mechanism can effectively influence individuals’ bidding behaviors. Economic auction mechanism, with realistic significance for market efficiency, can improve market efficiency without the need of efforts from bidders themselves. If both auction mechanisms which are tested online deliver a positive effect on bidder’s overbidding, these two auction mechanisms’ modifications should be taken into consideration in reality. The result from my experiment is presented in later sections to show whether whose two auction mechanisms can improve “winner’s curse”. In order to explicitly show the influence of notification, baseline auction is involved in experiments under which “winner’s curse” original magnitude can be measured. Instead of using concrete items to bid, the items’ values are only shown numerically, so that preference is not a factor need to be considered. What is more, a proper financial incentive system is designed for bidders, so bidders’ bidding
behavior should be pretty much like their real life’s decision. After finishing the experiment and data analysis, it is concluded that cheap talk can significantly influence the bidder’s behavior. On the contrary, for the sequential order mechanism, it does not significantly alleviate the winner’s curse through our online experiment.
The paper is organized in the following manner. In the following part, important literature related to the experiment is illustrated and my contribution will also be referred to.
Experimental design and subjects’ recruitment are described in details in the third part. Experimental data, result’s data analysis and my reflection about my thesis are provided in the fourth part. Last but not least, in part five, there will be a brief conclusion about the paper and discussion about what further research can be conducted based on my research.
2 Literature
In order to test whether two mechanisms are effective, two contrasting experiments are designed. During the experiment, subjects need to complete 15 repeated auctions in each round. For one contrast experiment, a notification of what winner’s curse is and why it occurs is shown before the start of every auction in a round, while another round does not give notification during the experiment. For another contrasting experiment, signals’ order is based on their corresponding items’ true value sequence which is sorted in either ascending order or descending order. Related literature is listed below so as to reach a robust hypothesis.
2.1 Anchoring effect
Tversky and Kahneman (1974) had studied about judgement under uncertainty which has firstly involved anchoring effect. According to the study, failing to adjust from an anchoring causes systematic and predictable errors and it was also pointed out that different starting points can make different estimates. They have done a research about the numerical impression about a sequence. Two group need to calculate a product in five seconds. One group was shown “8×7×6×5×4×3×2×1” and the other group was shown
“1×2×3×4×5×6×7×8”. The result reveals that the estimated product for descending sequence is significantly larger than the estimated number for ascending sequence and is more than four times the number of ascending sequence.
Northcraft & Neale (1987) they have launched a study about estate estimation which expert and amateurs make pricing decisions about real estate properties. What they have found is that the anchoring effect is robust for both expert and amateurs. Many researchers have
proved the robustness of the anchoring effect in different industries. Thorsteinson et al. (2008) have conducted experiments about the effect of irrelevant anchors on performance judgments in laboratory and field study and both studies have proven the robustness of anchoring effect. They also point out that the anchor can be distinguished by high applicable anchor and low applicable anchor. High applicable anchor has a more considerable anchoring effect on
subjects. According to Van Exel et al. (2006), it is demonstrated that the higher the ambiguity, lower involvement with the problem and a more trustworthy source, subjects are more likely to be affected by anchoring effect.
In sequential order mechanism, signals’ order is based on the items’ true value sequence. The difference between my paper and formers paper is that in previous research, they only ask subjects to write down their impression after presenting a sequence. In contrast, subjects need to write down every bid in every auction after presenting a signal in my experiment, which means they need to write down numbers during presentation of sequence and I will compare the bids’ sequence between subjects after data collection to see if this way of presenting can make a significant influence on subjects’ behavior. In accordance with articles described above, sequence arrangement has an effect on individuals’ numerical impression and decision making. The students who can be regarded as amateur bidders may be severely influenced by the anchoring effect in a laboratory environment. Consequently, the bids submitted in
descending order mechanism can considerably larger than the bids submitted in ascending order mechanism.
2.2 Cheap talk script
In light of Ronald G. Cummings and Laura O. Taylor (1999) they introduce an experiment design which is called “cheap talk” in the hypothetical bias experiment. In their experiment, they aim for eliminating hypothesis bias, which is the significant differences between responses to the real and hypothetical valuation questions. Instead of changing the
questionnaire format as Loomis et al. (2011) put forward, they inserted information about what hypothetical bias is and why it might happen. And this design is called as “cheap talk” script in their experiment design. Based on their data, they found that the response to the cheap talk script are significantly lower than those in the hypothetical survey without the cheap talk. The finding also passes the robustness test, in which the cheap talk script and experiment design have been change. And this is important for field application.
John A. list (2001) is the one who put this cheap talk script into practice and they try to overcome the shortcoming of Ronald G. Cummings and Laura O. Taylor (1999)’s paper. The responses in the real environment may be distinctly different from responses in a lab
environment. The study takes place in a well-functioning marketplace where sportscards are auctioned off, regarding to experienced and non-experienced bidders. He indeed found the positive influence of cheap talk on hypothesis bias, while this conclusion is not suitable for
experienced bidders. With respect to experienced bidders, the cheap talk is unable to change bidders’ behaviors.
In my experiment, subjects are recruited from the University of Amsterdam, with diversified majors and grades. Referring to the experiments conducted by Loomis et al. (1994) and John A. list (2001), subjects basically can be regarded as non-experienced bidders and are likely to be easily affected by cheap talk script. In my experiment, I use the format of cheap talk script from previous papers. What makes my paper different from the previous paper is that my experiment is an online auction and this cheap talk script is firstly used in the online first-price auction. As a result, I would like to hypothesize that the bids obtained from cheap talk script treatment should be significantly different from the group without cheap talk script.
3 Methodology
3.1 Basic auction design
Basic common auction design is described as below. In every item’s auction, a unit of goods is sold to the highest bidder and for each item, bidders only need to submit bid once. Each series contains two rounds auction and in each round, there are 15 items to bid. In each item’s auction, the value ( ) of the item is drawn from interval and each number within interval has same possibility to be drawn from the interval. Instead of knowing the true value of item, subjects only know a signal ( ) of true value. The signal is randomly drawn from a uniform distribution on interval . Given a signal, subjects should know that true value can be lower as well as higher than signal. The true value’s maximum value can be and minimum value can be , so the possible range for true value is
.
Signals are private and can be different from person to person. Subjects know that signal is private information and other information including how real value is produced and how many bidders they are competing with are common knowledge. After all subjects complete experiment, they will received an Email about if they are selected to be paid in cash. Then experimenter will contact the bidders who are going to be paid.
There is an example for one item’s auction
Your signal for item 1 is 225, please enter your bid for this item.
________ V [€50,€250] [€50,€250] s [V− €10,V + €10] s+ €10 s− €10 [s− €10,s + €10]
Table 1. The summary of experimental design
Treatment 1 ( Sequential order mechanism )
Treatment 2 ( Cheap talk
mechanism )
Series 1 Series 2 Series 3
Valid participants' population (total number of participants) 11(25) 12(30) 17(53) Round 1’s signal data sets
Signals are ordered by ascending true value’s sequence
Signals are ordered by descending true value’s sequence
Signals are ordered by random true value’s sequence
Round 2’s signal data sets
Signals are ordered by descending true value’s sequence
Signals are ordered by ascending true
value’s sequence
Signals are ordered by random true value’s sequence
Common ground and difference
Series 1 and series 2 have same set of items' true value, but the signals are different in
different round
For round 2, a notification shows up before every auction, while round 1 does
not contain cheap talk script
Notes: Treatment 1 aim for test the influence of sequential order mechanism and Treatment 2 is conducted to test the effect of Cheap talk script mechanism. There are 3 series auctions in total and each series contains 2 rounds. Each participant is only allowed to join one of the three series auctions. Valid participants’ population means the number of participants who choose all the correct answer of test questions and complete the whole auctions. Total number of participants means how many people have tried to complete the experiment. The test questions are presented in later part.
There are three series of the auctions in total and each auction contains two rounds. Each subject is only allowed to attend one series of the auction. Series 1 and series 2 both are designed for sequential order mechanism and series 3 are designed for cheap talk mechanism. The designs are shown in table 1. In order to simplify experiment, the signals are not
generated during the experiment, while signals are the same for everyone when subjects are doing the same series. Moreover, I only generate one set of random true values which contains 15 values and then based on that set of true value, I generate two sets of signals. I
call these two sets of signals are signals’ group 1 and signals’ group 2. Both signals’ group 1 and group 2 will be ordered by ascending true values’ sequence and descending true values’ sequence as I described in table 1. As a result, there will be two different signals sequence for each signals’ group. In addition, in order to not be observed by subjects that how signals are arranged, series 1 round 1 and series 2 round 1 share the same set of signals and at the same time, series 1 round 2 and series 2 round 2 share another set of signals. In this case, we can directly compare the experimental result of series 1 round 1 and series 2 round 1 as well as series 1 round 2 and series 2 round 2. All the data sets will be attached in the appendix. Each participant follows the procedure of experiment as below. First of all, bidders need to read the instruction carefully. If participants have a question they can ask the experimenter and will be answered in private. After reading the instructions, then click next page and there are three questions to test if they have totally understood the instruction. If they don’t select all the right answers, they cannot continue the experiment. In step 3, after they answer all correctly, there will be a pilot auction for them to exercise. Fourthly, participants do 15 items’ online auction in a single round. In step 5, after round 1, subjects have approximate one minute break and then start round 2 which contains 15 items’ auction as well. Last but not least, at the end of the experiment, the subjects’ Email address is asked if they want to have a chance to be paid in cash.
3.2 Subjects’ recruitment
Subjects are all students and are currently enrolled in the University of Amsterdam. Due to financial and lab rental limitation, subjects do not take experiment at the same times, whereas they will do the experiment one by one. Subjects receive a website link from Qualtrics which is a sophisticated online survey software. I am a supervisor who sit beside subjects when they are completing experiments and I make sure they finish all the steps and are not affected by the surroundings environment. The experiments last averagely 15 minutes for subjects and they will leave their email address at the end of experiments for contact if they are selected to be paid.
They knew at first that they have initial endowment 200 euro. They cannot continue experiments if their endowment is below zero and their data will not be included into final
data analysis. In each round, any profit they earn from the auction is added to into initial endowment. After all participants complete the experiments, three participants will be randomly selected to form a group and participants’ payoff will be calculated by comparing bids within the group. Every subject is only allowed to participate in one series auction. Fifty percent participants have a chance to be paid in cash based in one random round’s final payoff. The real amount of money paid in cash calculated as below.
(amount money paid in cash) = [(initial endowment) + (earning)]/20
In order to make sure that every participant completely understand the instruction, there are three questions to test as well as a pilot auction. Any of three questions are answered wrongly, subjects cannot join the experiment anymore. The test questions are shown as below.
1. Will you know the true value of each fictitious item? A. Yes B. No
2. The true value of a fictitious item is €100 and your signal is drawn from an interval. Which interval is correct as shown below?
A. [95, 105] B. [90, 100] C. [90, 110] D. [100, 110]
3. If you do not get item in an auction, will your total payoff change? A. Yes B. No
3.3 Mechanism design
3.3.1 Sequential order mechanism
As we have discussed in the literature section, ascending and descending sequential orders can have a different impact on subjects’ numerical impression and then influence individuals’ decision making due to the anchoring effect. Therefore, I would like to know if mechanism contains different true values’ sequence, can this mechanism diminish the magnitude of “winner’s curse”. As I described in experimental design, signals are not generated during the experiment, while signals are the same for everyone when subjects are doing the same series. Three sets of signals are generated based on corresponding true value’s sequence. What is more, two sets of signals will then be ordered by either ascending true values’ sequence or descending true values’ sequence. In this case, there are total four rounds’ signals’ sequential are generated. And the data set will be attached in the appendix.
Series 1 round 1 and series 2 round 1 share the same set of signals and at the same time, series 1 round 2 and series 2 round 2 shares another set of signals. Under such circumstance, the experimental data collected from series 1 round 1 and series 2 round 1 can be directly compared to each other. For series 1 round 2 and series 2 round 2, the situation is the same. If the bids are significantly different between series 1 round 1 and series 2 round, then the sequential order may improve “winner’s curse”. If not, I am unable to prove that sequential order may improve “winner’s curse”.
3.3.2 Cheap talk mechanism
As I mentioned in the literature section, notification about what “winner’s curse” is as well as why it might happen which is settled prior to auction is also can be called “cheap talk” script. “Cheap talk” originally indicates the communication between players. Because it takes nothing to get information from talk and this kind of talk does not have a direct impact on players’ payoffs. In contrast, according to the paper by Ronald G. Cummings and Laura O. Taylor (1999), they created a “cheap talk script” into experiments can significantly influence subjects’ behavior. This type of reminder can be regarded as an effective method to improve individuals’ behaviors.
In my experiment, series three contains 2 rounds. In the first round, there is no “cheap talk script”. In the second round, there is a “cheap talk script” before every auction to remind people. I try to draw a conclusion by comparing the group with “cheap talk script” and without “cheap talk script”. In order to effectively convey the concept of the winner’s curse, the notification is shown before every fictitious item’s auction.The context of notification is displayed in following.
Winner’s curse is a phenomenon that might happen in common value auction. Assume that all bidders make unbiased estimation of an item and bids are an increasing function of these estimates. the bidder who wins the item tends to have the most optimistic estimation of item’s value. As a result, the winner is likely to bid more than item’s real value and then make below normal or even negative profits.
4 Results
4.1 Summary of experimental data
Table 2. The summary of collected experimental data
Series 1 Series 2 Series 3
Round 1 Round2 Round 1 Round2 Round 1 Round2
Valid Number of subjects (total number of
subjects*)
11(32) 11(32) 12(40) 12(40) 17(52) 17(52)
Mean true values 150.00 150.00 150.00 150.00 149.67 149.67
Mean signals 149.87 148.87 149.87 148.87 151.87 149.67
Mean bids 142.32 143.05 142.68 140.45 148.15 140.60
Standard deviation 15.37 13.48 14.80 12.34 20.97 21.08
The total number of bids larger than true value (15 items in each round)
52 42 64 45 91 67
Notes: All figures are rounded to two decimal places.
Standard deviation is calculated based on all the bids within same round.
*Total number of subjects means all the subjects who have participated experiments and includes some subjects who have not finished the whole experiment. Valid number of subjects means how many subjects’ data can be taken into analysis.
Table 2 summarizes the experimental data which is collected from the two contrasting experiments. The first row shows how many subjects have completed the whole experience. As illustrated in Table 1, series 1 and 2 both are designed for sequential order treatment and the difference is the data sets. Only when subjects have completed the whole experiment, then their experimental data is valid and will be processed. The number in bracket
demonstrates the number of all subjects who have participated, so it includes invalid data. Some subjects may fail test question or didn't complete the whole experiment. The second row and third row indicate the average true values and average signals, respectively. During
the experiment, true values(V) are all randomly drawn from a uniform distribution on interval and all the signals are randomly drawn from a uniform distribution on interval
. what is more, to simplify the experiment, values and signals are totally same for subjects who participate in same series. By comparing the mean of true values and signals, it can be seen that the experimental data of the three series have pretty much identical
distribution. As a result, we can roughly compare the mean of all bids at first in order to see if there is a big difference between treatment group and baseline group. The fifth row describes the data’s variation or dispersion. The standard deviation is quite similar between series 1 round 1 and series 2 round 1, series 1 round 2 and series 2 round 2. In the meanwhile, the standard deviation of series 3 round 1 and series 3 round 2 are quite similar as well. In this case, it can be concluded that with same data set but different sequential order, the dispersion of all bids is very similar. The last row notes that how many bids are larger than
corresponding true value which partially reveal the magnitude of winners’ curse. If bidders win an auction with over-value bid, they definitely will lose money. In this situation, even though items are obtained, it is not worthwhile for auctioning off the item.
According Vickrey (1961)’s RNNE model which shows a symmetric risk neutral Nash equipment for first-price auction and Cox et al. (1982)’ CRRAM model which modifies RNNE model, bidders should make discount for signals based on number of rivals. People who always make a discount for signals do not need to worry about losing money. For last row, there are 15 items for each round and then multiply the number of subjects, the product is the total number of bids. For example, the series 1 round 1 has 11 subjects and then multiply 15, the product 165 is the number of total bids in this round. 52 divides by 165 can get the percentage of bids that are larger than true value.
Comparing series 1 and series 2, we can sketchy conclude the effect of sequential order treatment. According to data sets, we know that series 1 round 1 and series 2 round 1 have same signals and true value array, same circumstance for series 1 round 2 and series 2 round 2. The only difference between series 1 round 1 and series 2 round 1 is that signals are ordered by either ascending true value’s sequence or descending true values’ sequence. The average bid of series 1 round 1 and series 2 round 1 is quite similar and latter one is a little bit higher. Nevertheless, the average bid for series 1 round 2 and series 2 round 2 is considerably different. What is noticeable is that subjects in descending order treatment bid averagely less
[€50,€250]
than bids in ascending order treatment. The difference is more considerable by comparing series 1 round 2 and series 2 round 2. In accordance with literature section, it can be known that descending sequence can leave individuals an impression of larger numerical value compared to ascending sequence. The mean of bids is supportive of this theory, however the number of bids larger than true value is inconsistent with this theory. The number in series 1 round 1 is smaller than the number in series 2 round 1, while the number in series 2 round 2 is larger than series 1 round 2. This shows that descending sequence treatment does not have a bigger number of bids that are larger than true value compared to ascending sequence treatment.
In series 3, we can compare the round with and without cheap talk script. It can be easily seen from the table 2 that with notification, bidders are likely to bid much more when compared to bids in round without cheap talk script. By making a contrast for mean bids between series 3 round 1 and series 3 round 2, the averaged bids is considerably higher in round without cheap talk script. As mentioned in the section two, Ronald G. Cummings and Laura O. Taylor (1999) put forwarded cheap talk script and they proved that cheap talk script has a significant influence on participants’ behavior, especially for inexperienced bidders. The experimental result is consistent with the conclusion made by Cummings and Taylor. By contrasting with the number of bids that are larger than corresponding true value in round without cheap talk script, the number is considerably less in the round with cheap talk script. Both mean bids and overbids reveal that cheap talk script can modify human beings’ behavior.
4.2 further analysis
Figure 1: Averaged bids in Series 1 Round 1 Figure 2: Averaged bids in Series 1 Round 2 and Series 2 Round 1 and Series 2 round 2
Figure 3: Averaged bids in Series 3 Round 1 and Series 3 Round 2
I calculated the averaged bids for each item and draw figures for each comparable pair of rounds. From item 1 to item 15, the true values go up, while the signals are not strictly ascending sequence according to previous data sets. In figure 1 and 2, an item with the same number represents same true value. In figure 3, the item’s number is not related to the item’s number in figure 1 and 2.
Figure 1 and 2 mainly describe how bidders react to the same signal and true value under different sequential orders. In contrast with series 1 round 1, series 2 round 1 has larger averaged bidding value between item 9 and item 11 and has smaller averaged bidding value between item 12 and item 15. Compared to series 1 round 2, series 2 round 2 has larger averaged bidding value between item 1 and item 8 and has relatively smaller averaged bidding value between item 10 and item 15. As a result, descending sequence causes larger bids in items with relatively small true value and causes small bids in items with
correspondingly large true value.
Through Tversky and Kahneman (1974), it can be obtained that “8×7×6×5×4×3×2×1” and “1×2×3×4×5×6×7×8” have different numerical impression on individuals. The descending sequence is inclined to provide a larger numerical impression compared to ascending
sequence. Nevertheless, the way I examine the impression is different from what Tversky and Kahneman have done. Subjects need to write done every “impression” for each item, while in Tversky and Kahneman (1974)’s paper, subjects only need to fill out only one number after presenting a whole sequence. From Table 2, we also obtained that descending order treatment basically has larger averaged bids than ascending order treatment.
Taking a further look at graph 2, we can find out that there is an outlier which is significantly larger than the other round’s value. I check all the bids in that round and then I find out that one bidder has made an incredible large bid for item 7 which is already exceed the boundary of true value’s generation interval. As a result, it makes sense that why mean bids of series 1 round 2 is significantly larger than that in series 2 round 2. Due to small sample, the outlier is very influential for summary of experimental data.
Graph 3 generally describes how bidders behave when they are confronted with cheap talk script or without cheap talk script. It can be concluded from table 2 that bids in cheap talk script treatment are considerably smaller than bids in round without cheap talk script. What is more, no matter the mean bids or the number of bids that are larger than true value, both of them are in favor of this theory mentioned in the literature section. Just by observing the Graph 3, we can get a pretty much similar conclusion that cheap talk script can significantly influence bidders’ behavior and mitigate the magnitude of the winner’s curse. From item 2 to item 15, bidders make relatively larger bids under cheap talk mechanism. The largest
by item 7, which is 20.41 and 19.11, respectively. Item 7 has relatively big value and item 8 has relatively small value. Consequently, it is hard to say that whether large value and small value make different effects.
Table 3: Significance test for comparable rounds
T-test of means Degree of freedom
Series 1 round 1 versus
series 2 round 1 -1.13 21
Series 1 round 2 versus
series 2 round 2 0.91 21
All bids in ascending order’s treatment versus
Bids in descending order’s treatment
-1.47 44
All bids in ascending order’s treatment versus
Bids in descending order’s treatment (item 1 - item 7)
-0.84 26
Series 3 round 1 versus
series 3 round 2 3.59* 16
Notes: The H0 for t-test of means is that two samples’ mean is same, which can be written as:
, where represents sample’s mean bid for each item and means two different samples. The can been written as: , where and have same meaning as mentioned above. Row four use paired-sample t-test due to same objects are tested twice. According to paired-sample t-test, the degree of freedom should be 16.
* means Significantly different values at the two-tailed p < 0.05 level. T-test is for sample size less than 30.
H0: xi= xj x i, j
Table 3 summarizes the t-test has been made for the experimental result. Row 1 and row 2 have the same true values’ array but different signals’ array. The t-test of means for row 1 and row 2 are -1.13 and 0.91, respectively. Both of them are not significant at the p<0.05 level. Although from table 2, it can be seen that descending sequence can make relatively larger mean bids. However, from the above analysis, it is known that an outlier in series 1 round 2 substantially influence the mean bids. As a result, sequential order mechanism is not proved that it can significantly improve bidders’ behavior and then mitigate winner’s curse. The third row compare all the bids in ascending order’s treatment with bids in descending order’s treatment. According to Table 2, we knew that the true value for rounds in sequential order treatment is the same and their averaged signals is very close to each other. In this situation, all the bids in descending order’s treatment can be compared to bids’ in descending order’s treatment. With a larger sample size, the result of the t-test is -1.47 which is not significant at p<0.05 level. This result is consistent with the result of row 1 and 2. From previous analysis, we know that descending order’s treatment has relatively larger value in low number. As a result, I test the significance between item 1 to item 7. However, as the row 4 shows, there is no significant difference between bids in descending order’s treatment and ascending order’s treatment.
The t-test for series 3 round 1 versus series 3 round 2 is 3.59, which is significantly different at the p<0.01 level. Round 1 is without cheap talk script and Round 2 is with cheap talk script. In this case, it can be concluded that cheap talk script has a positive influence on human beings. Bidders are more likely to bid significantly less under cheap talk script’s treatment. From the previous analysis, the conclusion is pretty much same no matter with regard to mean value or t-test. What is more, the graph 3 also conveys the same message. For inexperienced bidders, cheap talk script mechanism is effective for modifying bidders’ behavior. In this case, we can say that cheap talk script mechanism is robust and should be taken into consideration to be generalized in real life.
5. Discussion and conclusion
In summary, I use first-price common value auction to test if the two auction mechanisms I designed reduce the magnitude of winner’s curse. Only one-shot auctions are involved in the experiment. Based on anchoring effect, I design a mechanism that in a series of auctions, the signals of the items are ordered by true value’ sequence of either ascending order or
descending order. According to the experimental result, subjects do not react significantly differently to different sequential order treatments. Even though I find that in relatively small values’ items, descending order seems to have larger bids, I have not test out any significant difference between ascending order and descending order’ treatment group. In the light of G. Cummings and Laura O. Taylor (1999)’ cheap talk script’ experimental design for
eliminating hypothetical bias, I want to use this script to eliminate the winner’s curse as well. A notification about what winner’s curse is and why it occurs is shown before every one-shot auction. In terms of result, I find that bids in cheap talk script is much smaller than bids in treatment without cheap talk script. No matter from data of mean bids comparison or
significance test, the results are in consistent with each other. In this case, I think that for non-experienced subjects, cheap talk script can modify their behavior while sequential order has not effect on subjects’ behavior.
However, there are some limitations in my experiment. Due to resource constrains in terms of money and time, I only conduct the experiment with small sample and the subjects are all students who are recruited from university.With small sample, one outlier data is likely to influenced the experimental result substantially and sample may lack of representativeness. What is more, I only test the effects of chap talk scripts among non-experienced bidders and in accordance with John A. list (2001)’ paper, experienced bidders are not likely to be influenced by cheap talk script. In this case, cheap talk need to be tested on experienced bidders to prove its robustness across people of varied types. In addition, online auction only lasts around 15 minutes and the subjects pay much attention on illustration presented on screen. While in reality, the circumstance can be totally different. It takes hours for a series of auctions, during which time bidders may loss attention on this time-consuming process and cheap talk is no longer effective. In terms of sequential order mechanism, the true values are drawn from a uniform distribution on interval [€50,€250], of which the gap between the
number of boundaries is not substantial. In another word, the difference between the impression of descending order and ascending order can be too subtle to be detected. In future research, more field studies need to be done on these mechanisms to prove their practical significance. These two mechanisms need to be done on experienced bidders to address if those mechanisms work on experienced bidders. Sequential order mechanism with varied internals also need to be tested on both experienced and non-experienced bidders in real auction. Cheap talk script with varied formats can be tested to prove whether the effect of cheap talk is still robust across different types of formats. When auction is conducted in reality, complicated factors should be considered to improve the efficiency of auction market. Future research should address more mechanisms in which detailed factors are involved and the winner’s curse of professional bidders as well as non-experienced bidders can be
Appendix A: Subject’s instruction and
online auction’s format
This is an experiment about decision making. If you follow the instruction carefully and make good decisions you may earn a considerable amount of money. Now, you are participating an online auction and you are going to bid for online goods (presented numerically, not real object) in two periods. Each period contains 15 fictitious items to bid and the only thing you need to do is submitting your bid for each item just once. Your bid for each item will be compared to two other bidders’ bid who are randomly selected from all participants. The bidder who has the highest bid will get the item and has to pay
the highest bid value. And his/her profit is calculated as below: (value of item)- (highest bid) = profit
For other bidders who do not get the item, his/her profit is equal to zero.
In each item’s auction, the value ( ) of item is drawn from interval and each number within interval has same possibility to be drawn from the interval. Instead of knowing the true value of item, subjects only know a signal ( ) of true value. The signal is randomly drawn from a uniform distribution on interval . As a result, your signal can above the true value as well as below the true value. You do not know the exact value of item and your need to make your decision based on your private signal.
There are two rounds in total and at the beginning of each round, your initial endowment is 200 euro. You cannot continue experiments if your endowment is below zero and your data will not be included into final data analysis. Any profit (can be negative) you earn will be added to initial endowment. After all participants complete the experiments, three
participants will be randomly selected to form a group and your payoff will be calculated by comparing bids within the group. Fifty percent participants have chance to be paid in cash based on one random round’s final payoff. The real amount money paid in cash calculated as below.
(amount money paid in cash) = [(initial endowment) + (earning)]/20
V [€50,€250]
[€50,€250]
s
In the following, there are three questions to be tested in order to know whether you have fully understood the instruction. Any of three questions are answered wrongly, you cannot join the experiment anymore. The test questions are shown as below.
4. Will you know the true value of each fictitious item? A. Yes B. No
5. The true value of a fictitious item is €100 and your signal is drawn from an interval. Which interval is correct as shown below?
A. [95, 105] B. [90, 100] C. [90, 110] D. [100, 110]
6. If you do not get item in an auction, will your total payoff change? A. Yes B. No
Congratulations! You have chosen all correct answers. And then there is a pilot auction for you.
In this pilot auction, your signal for this item is 140, please enter your bid for this item. _________
In last auction, the really value is 141. If you are the highest bidder in last auction, you will get the item. the profit you earn is:
144- (your bid) = profit
If you enter a bid higher than 141, you have negative profit. If you enter a bid lower than 141, you have positive profit.
In following auctions, you will see same question format for each item’s auction and you need to write down every bid for each item.
Appendix B: Data sets for each series
Series 1 Series 2 Series 3
Round 1 Round 2 Round 1 Round 2 Round 1 Round 2
Ture
value Signal value Ture Signal value Ture Signal value Ture Signal value Ture Signal value Ture Signal
Auction 1 101 93 199 197 199 194 101 100 225 225 225 233 Auction 2 108 117 192 199 192 198 108 108 99 101 99 94 Auction 3 115 112 185 175 185 191 115 114 150 155 150 148 Auction 4 122 114 178 176 178 170 122 130 72 73 72 80 Auction 5 129 127 171 166 171 175 129 129 182 187 182 172 Auction 6 136 130 164 167 164 170 136 127 113 114 113 112 Auction 7 143 144 157 152 157 160 143 137 218 224 218 210 Auction 8 150 153 150 156 150 153 150 156 141 144 141 131 Auction 9 157 160 143 137 143 144 157 152 115 113 115 118 Auction 10 164 170 136 127 136 130 164 167 161 169 161 169 Auction 11 171 175 129 129 129 127 171 166 146 148 146 154 Auction 12 178 170 122 130 122 114 178 176 190 190 190 188 Auction 13 185 191 115 114 115 112 185 175 107 101 107 101 Auction 14 192 198 108 108 108 117 192 199 222 231 222 230 Auction 15 199 194 101 100 101 93 199 197 104 103 104 105
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