Experiment Set-Up

In the experiment, two different auction settings were used. The designs for both settings were chosen from the second simulation study (presented in section 8.2) to allow for direct comparison to the simulated auctions. Also all the parameter values were set to be the same as in the simulations studies (5 items, 600 units of each item, 2% decrement). In the simulation study we tested 48 different designs, which could not have been reproduced with a limited number of human subjects. Thus, I chose two of the designs, one design with equal capacities, and one with unequal capacities, since based on the simulation study it was the bidders’ capacities which had the biggest impact on the efficiency of the auction outcome.

For the first experiment setting – auction A – I chose an equal capacities auction with 15 bidders, normal economies of scope, and full shortlist. The initial bids were created based on advantage in variable costs (Bid1). In the simulation study, the efficient allocation changed from replication to another (there were 50 replications of each design). For the laboratory experiment I chose only one replication, that is, one set of cost functions. Using the same cost functions for each group of participants allowed for better comparisons between the groups. I deliberately chose a replication which had ended in the efficient allocation in the simulation in order to see if the auctions would end in the same, efficient allocation with real users as well.

21 I am solely responsible for the design and conduct of the laboratory experiment as well as for the analysis of the results.

For the second setting (auction B) I chose the corresponding unequal capacities auction (15 bidders, normal economies of scope, full shortlist and initial bids created based on Bid1). However, this time I chose a replication in which the winning allocation was inefficient (winners’ combined production costs were 9.2% above the costs of the efficient allocation), in order to study whether human users could direct the auction to a more efficient allocation or not.

Experiment Participants

In total 74 students – both undergraduate and graduate students – participated in the experiment. The students were all participants of a course on managerial economics at Helsinki University of Technology. Thus, the students were already familiar with the concepts of production and cost functions, and economies of scale and scope.

However, only 14 of them had participated in online auctions before, and the combinatorial auction was an unfamiliar concept to all of them. Each student was required to participate in two auctions: first in one A auction and then in one B auction. All 74 participants bid in the first (A) auction, but only 69 of them bid in the second (B) auction. The students were rewarded by giving them points that counted towards their final grade from the course. In the beginning each student received 5 points, and they were rewarded extra points for playing well (winning with a profit larger than their counterparts), and for answering a post-experiment questionnaire. In case the students did not perform as expected (for example, placed unprofitable bids or failed to win when they had the chance to), points were deducted from them. The maximum score attainable was 11 points, which is 11% of the final grade from the course. Giving credit for participation is an easy and cheap way of motivating students to participate in laboratory experiments.²²

Prior to the experiment, all participants were required to participate in a briefing session. The briefing session contained some general theory on combinatorial auctions.

Also, the students were briefed on how to use the CombiAuction system, how the support tools work, and how to use the cost function parameters given to them on an

22Also Bichler (2000) gave students credit for participating in his experiments.

Excel sheet to calculate their costs for each bundle. It was explained to the students how the winners are determined in a reverse combinatorial auction, and what principles the QSM is based on (and why it is not available at the beginning of the auction). However, no mathematical notation or formulations of the WDP or the QSP were presented.

The Organization of the Experiment

The experiment was organized in four sessions during four consecutive days so that there were two sessions (days) for A auctions: A1 and A2, and two sessions (days) for B auctions: B1 and B2. The reason for having two sessions for both auctions was to offer the students the possibility to choose the days that suited their schedule the best. Each auction lasted for 23,5h (or longer if the closing time was extended). The participants were physically in different locations during the auction, but participated over the Internet. The duration of 23,5h is longer than the 1-4h duration usually used in laboratory experiments (in which the participants usually are in the same place at the same time). However, I chose such a long duration to better simulate an actual online auction in which the endogenous arrival of bidders is a key characteristic. Real online auctions usually last for several days or weeks, partly in order to give time for potential buyers to find the auction. However, since in this experiment the bidder pool was predefined and the prospective bidders were all knowledgeable about the auction, there was no need to extend the auction longer than was needed to be able to observe different bidding strategies. The auctions began at 5pm and the scheduled closing time was 4.30 pm the following day. This way the bidders had essentially two days time to place bids, which I anticipated to be enough to separate early bidders from late bidders.

Even though the simulated auctions, from which I borrowed the design parameters, cost functions and capacities, all had 15 bidders, I chose to divide the students into smaller groups. There were two reasons for this. Firstly, that way I could get more replications of the auctions. Then, if for some reason some of the auction outcomes were distorted (e.g. due to mistakes made by the bidders) there would be enough data left to analyze. Secondly, I thought it would be more rewarding for the students if a bigger portion of them could win at least once during the experiment. For the A

auctions, 46 students enrolled in session A1, and 28 students in A2. Thus, I divided the A1 participants into 9 groups of 5 students, and one group of 6 students, and A2 participants into 4 groups of 7 students. Five students were enough to guarantee sufficient competition in equal capacities auctions in which the efficient allocation consisted of two bidders. Even if bidders placed bids for smaller bundles than maximum capacity, it would be very unlikely that all five bidders would be provisional winners simultaneously. For the unequal capacities auctions five bidders might not have been enough, since the bidders’ capacities were smaller than in the equal capacities auctions, and more bidders would always be needed in the winning allocations. Thus, the 40 participants in the B1 session were divided into 4 groups of 7 students and 2 groups of 6 students, and the 24 participants in the B2 session were divided into 4 groups of 7 students and one group of 6 students.

The students were assigned cost functions to identify them. From the 15 bidders in the simulations I chose 5-7 bidders to be assigned as identities to the students. The same bidder identities (cost functions) were used in all the groups to allow for direct comparisons between groups. This way I could compare the auction outcomes (efficiency and total cost to the buyer) to see if they differed from one group to another – even though the starting points were equal. Also, when the same bidder identities were used in each group, the bidders’ performance could be compared with corresponding bidders in other groups. This comparison determined the participants reward points. For the equal capacities (A) auctions with five bidders I chose the cost functions of the two bidders, who formed the efficient allocation (Bidders 12 and 15) ²³. In addition I chose the cost function of one bidder (Bidder 10) whose cost for the efficient allocation bid (300, 300, 300, 300, 300) was close enough to the efficient bidders so that a “pseudo efficient” allocation could be reached. A pseudo efficient allocation was defined as an allocation which was not efficient, but in which the total cost to the buyer was within the 2% decrement of the efficient production costs. In the pseudo efficient allocation the efficient bidder(s) cannot afford to submit new bids because in order to reduce the buyer’s cost by 2% they would have to incur a loss. The

23 The bidders’ numbers refer to their number in the simulated auction, which makes is easy to keep track of the bidders’ costs.

two remaining bidders whom I chose (Bidders 5 and 8) had higher costs, and they should not be among the winners. When there were 6 or 7 participants in the auction, the extra bidders were assigned costs that could also result in pseudo efficient outcomes (Bidders 1 and 11), but who had higher costs than Bidders 12, 15 and 10. The bidders’

cost function parameters are presented in Appendix 4.

In the unequal capacities (B) auctions I included the bidders from the efficient allocation (Bidders 3, 8 and 13), the bidders who won in the simulated auction (Bidders 4 and 15 in addition to Bidder 3), and the remaining one or two bidders were chosen at random to be Bidders 1 and 9. In the unequal capacities case it would have been impossible to try to deduce which bidders could create a pseudo efficient allocation, since the item combinations in the winning bids also would have to change due to the different capacities (in the equal capacities case the winning bids would almost always be for half the total demand). The bidders’ cost function parameters and capacities are presented in Appendix 4.

The organization of the experiment is summarized in Figure 15. The participants were divided into A1, A2, B1 and B1 sessions according to their preferences. I then further divided them into smaller auction groups within each session. In each auction there were the same set of cost functions (bidder identities) given to the participants. The cost functions were assigned randomly in the A auctions, but in the B auctions I tried to give better cost function to those who had received the worst ones in the A auction.

This way I tried to give everyone equal chances to obtain extra points. Everybody participated first in one A auction and then in one B auction. The equal capacities (A) auctions were slightly simpler bidding environments, hence they also served as a practice session for the B auctions. The participants were grouped differently in the A and B auctions. The idea was to have bidders bid against new competitors – who maybe used a different strategy – in the second auction. Also, due to the participants’

diverse preferences and different group sizes, it would have been impossible to maintain the same groups in both A and B auctions.

AUCTION EXPERIMENT

Figure 15 The organization of the laboratory experiment