Silviase/jgov_v1.4_full_ann huggingface dataset:
7) The expected profit for defect and not report ( $ E\pi_{dnr} $ ).

$$ E\pi_{d n r}\quad\mathrm{i s~t h e~s a m e~a s}\quad E\pi_{d f} $$

8) The expected profit for defect and report ( $ E\pi_{dr} $ ):

$ E\pi_{dr} $ is the same as $ E\pi_{d} $ since the player does not have to pay the fine by reporting.

Comparing these four expected profits, we can tell immediately that it is not rational to choose the “defect and not report” for player i since $ E\pi_{dr} $ always exceeds $ E\pi_{dnr} $ .

To know in what condition the collusion would be maintained under the leniency program, we compare the expected profits of the remaining three strategies. First, compare $ E\pi_{cnr} $ and $ E\pi_{cr} $ to examine whether a player who did not defect in bidding has an incentive to report or not. If $ \delta $ is larger than $ qz/(z-\varepsilon-c) $ , then it is more profitable for player i not to cheat the other players by reporting $ (E\pi_{cnr}>E\pi_{cr}) $ . Assume that this condition is satisfied. Now we compare $ E\pi_{cnr} $ and $ E\pi_{dr} $ to examine whether player i should defect in bidding rather than maintain the collusion. As we mentioned before, it is rather difficult to calculate the exact value of $ E\pi_{cnr} $ , which is the same as $ E\pi_{cf} $ . We can tell only that $ E\pi_{cnr} $ is larger than $ \underline{E\pi_{cf}} $ . Therefore, we use $ \underline{E\pi_{cf}} $ to compare with $ E\pi_{dr} $ and find a strict condition when keeping the collusion is more profitable than defecting. If $ \delta $ is larger than $ \left\{4(z-\varepsilon-c)+qz-\varepsilon\right\}/\left\{5(z-\varepsilon-c)-\varepsilon\right\} $ , then $ \underline{E\pi_{cf}} $ exceeds $ E\pi_{dr} $ , and it is more profitable for player i to maintain the collusion ( $ E\pi_{cnr} $ is strictly larger than $ E\pi_{dr} $ ). The question is whether such a $ \delta $ exists between 0 and 1. If $ (z-\varepsilon-c) $ is larger than qz, then there exists a $ \delta $ within the range. Since we already assumed that $ \delta $ is larger.
than $ qz/(z-\varepsilon-c) $ , $ (z-\varepsilon-c) $ is surely larger than qz. Therefore, leniency programs are not sufficient to deter cartels. Especially if a fine rate is too low, it is very possible that the leniency program does not have any impact on firms which are involved in cartels.

### 3. Experimental Design and Procedure

Our experiments were run at the Kyoto Sangyo University Experimental Economics Laboratory on December 17, 20, and 21 in 2005. Three sessions were run in total, and one session was conducted on each day. 67 subjects were recruited in total from among undergraduates of various majors. They applied for the experiment voluntarily through the Internet. We tried to recruit subjects whose backgrounds (major, year in school) were not similar, so that most subjects would not be put into a group with someone they already knew.

All experiments were run by computers. All the treatments were programmed and conducted with the software z-Tree (Fischbacher (1999)). We also used a free software program called "Minna no chat" that allows subjects to communicate online before price bidding.

In each session, there were four six-member groups. Five of the members in each group played the role of seller, and one member played the role of an observer for his group. $ ^{7} $ The role of buyer was played by the computer, which determined who bid the
minimum price in each group. If there was more than one seller who bid the minimum price, only one of those sellers was chosen randomly by the computer to complete the transaction.

We ran four kind of treatments: Benchmark, Communication, Antitrust, and Leniency. $ ^{8} $ The values for the parameters in the theoretical model were: the reserve price, z, is 200, the homogeneous marginal cost, c, is 100, the minimum bid increase (or decrease), $ \varepsilon $ , is 10, the probability of investigation by the authority, p, is 0.15, the fine rate, q, is 0.10. In each treatment, the auction game was repeated for 15 rounds. Subjects were not told the exact number of repetitions at the beginning of experiments. We told them that the auction game would be repeated for at least 12 rounds, and after the 12th round, the computer would decide randomly whether the game would be continued or terminated. The details of each treatment are explained below.

## Benchmark

This treatment is a competitive market where five sellers compete for one contract with one monopolistic buyer. $ ^{9} $ In this treatment, sellers are not allowed to communicate with each other before bidding. Each seller bids a price simultaneously and independently within the range of 100 to 200 with 10-unit increments.
## Communication

In this treatment, sellers can communicate with each other before bidding. At first, they decide whether they will enter the chat room or not. Each subject could chat only with same-group members, and not with people in other groups. There is no penalty for chatting (or bid rigging). The chatting time is limited to three minutes. After the communication stage, each seller bids a price simultaneously and independently as in the Benchmark treatment.

## Antitrust

This treatment is similar to the Communication treatment except that there is a fine against chatting. Each seller is investigated by a hypothetical antitrust authority (the computer) after the auction with the probability of 0.15. Similar to the Communication treatment, sellers first decide whether they will enter the chat room or not. If only one person entered the room, this was not considered as illegal communication. If more than one person entered the room, this was regarded as illegal communication and a fine was imposed on them if they were investigated. After the auction, the computer drew a lottery for each subject at the end of every round and determined who was investigated. If the investigated seller had entered the chat room and there was at least one other person in the room before bidding, he is given a fine. The fine is 10% of the winning price (gross profits) earned in the current round and any two rounds prior, only if the detected subject won the auctions. A fine can only be applied once per round. To illustrate, if a seller is found to be involved in collusion in the third round, then his fine is applied to his first, second, and third round profits. If the same seller is then found to
be in collusion in the fourth round, his fine is based only on his fourth round profits. As in the Communication treatment, the chatting time is limited to three minutes.

## Leniency

This treatment adds to the Antitrust treatment the possibility for sellers to apply for a leniency program. Similar to the Antitrust treatment, subjects who communicated with other group members are fined if they are investigated. Those who entered the chat room can decide whether they will apply for the leniency program or not after the auction. The first applicant can get full immunity from a fine, the second applicant can get 50% immunity, and the third applicant can get 30% immunity. People who did not enter the chat room or people who entered the room alone, do not have to move on to the leniency application decision.

A summary of the characteristics of each treatment is shown in Table 1. In each session, two treatments were run in sequence. The combination of the two treatments in each session is explained in Table 2. In each session, the Benchmark treatment was implemented first, and then one of the other treatments followed. That is, subjects experienced the competitive auction without communication first, and then they experienced a treatment with communication.

The experimenter read aloud the instructions in front of the subjects, who read along using their own printed instructions. $ ^{10} $ Subjects went through three practice rounds to get used to how to use the mouse and keyboard and how to understand their computer screen. In the Benchmark treatment, subjects were not allowed to make free
decisions in the practice rounds (they typed a certain input which was given by the experimenter). In other treatments with communication, subjects practiced how to chat online. We instructed subjects to input certain content first and then allowed them to input messages freely in the later practice rounds. $ ^{11} $ $ ^{12} $ No subject was forced to enter the chat room in the real rounds.

In all the four treatments, subjects were informed whether they won the auction or not, and the winning price was revealed to all subjects after the auction. However, bidding prices of other subjects were not revealed, and each subject could not know who was the winner if he was not the winner. At the end of each round, subjects could see the information of his own profits for the round. He was not informed of the information related to other people's profits. In the Leniency treatment, subjects who applied for the leniency program were informed how much immunity they could get, but not about how much immunity other subjects got. Subjects who did not apply for the leniency program were informed via their computer screens whether any other member in his group applied for the leniency program. Each seller had their own ID (“member 1,” “member 2,” “member 3,” “member 4,” “member 5”) in Communication, Antitrust, and Leniency. Their IDs were the same for each treatment throughout the experiments. The identities of the subjects were kept secret.
The fine scheme was designed to be similar to the JFTC scheme. The immunity schedule is also similar to JFTC’s leniency program. $ ^{13\ 14} $

Subjects were paid in cash individually after the experiment. The amount they were paid was determined by how much they earned in the experiment (the currency unit was called “dollar” in the experiment. One dollar was exchanged for 10 yen). The average earning was 2,873 yen (about 24.8 US dollars), the highest was 7,000 yen (about 60.3 US dollars), and the lowest was 2,500 yen (about 21.6 US dollars). Each session lasted about three hours. $ ^{15} $

### 4. Predictions

In this section, we compare the expected profits according to the theoretical model discussed in Section 2. Since subjects were told that the experiment would be repeated at least for 12 rounds, subjects might plan what to do for the first 12 rounds and calculate the expected profits for those rounds. For simplicity, we assume that subjects do not discount their profits.
In the Benchmark treatment, since subjects can not discuss bid rigging, it is predicted that they will bid 110 together from the early rounds. The expected profit for the first 12 rounds is just 24 $ (=12\times(110-100)/5) $ .

After experiencing such a competitive treatment, it is predicted that subjects will try to collude with each other in the next treatment (with communication) and bid 190 or 200. In the Communication treatment, if a subject does not enter the chat room (does not commit bid rigging) and bids 110 from the first period, the expected profits for this case for the first 12 rounds is the same as the one for the Benchmark treatment (=24). $ ^{16} $ If subjects commit bid rigging and bid the reserve price together and rotate the winner randomly in every round, the expected profits for this case is $ 240 (=12*(200-100)/5) $ . The expected profit for defecting from the first period (a bidder bid rigged, but cheated the other bid riggers by bidding 190) is 112. Therefore, it is more profitable for each subject to commit bid rigging in the Communication treatment.

In the Antitrust treatment, the expected profit for collusion is 232.8, while the expected profit for defecting is 109.15. Therefore, it is still more profitable for subjects to maintain their collusion.

In the Leniency treatment, the expected profit for colluding and not reporting is 232.8 (the same as the expected profit for colluding in the Antitrust treatment). The expected profit for colluding and reporting is only 42. The expected profit for defecting and reporting is 112 (the expected profit for defecting and not reporting is always dominated by the expected profit for defecting and reporting. See the discussion in
Section 2). Therefore, it is still more profitable to maintain collusion under the leniency program.

However, in the prediction above, we assume that subjects would give up collusion immediately as soon as any player defects or reports to the authority to punish the defector (trigger strategy). This assumption might be too strong, and the prediction might not be the same as the real behavior of subjects. In addition to that, maintaining collusion is only one of the equilibria. It is also an equilibrium that nobody commits bid rigging. Since it is not costly at all for subjects to enter the chat room, and the content of communication did not bind subjects to a specific price to enter in the bidding stage, chatting can be considered as merely cheap talk. In this case, subjects might behave as competitively as in the Benchmark treatment. Moreover, subjects might use a different kind of bid rigging scheme. $ ^{17} $ Therefore, we believe that experimenting on this sort of situation in the laboratory is helpful in observing plausible bid rigging schemes and what form an optimal leniency program might take.

### 5. Analysis of Results

### 5.1 Bid Prices and the Rate of Bid Rigging $ ^{18} $

Figure 1 compares the average winning prices of all treatments. The average winning price in Benchmark never went higher than 111, while the average winning price in the Communication treatment never went lower than 192.5. This shows the existence of fierce competition in the Benchmark treatment, and the existence of strong
collusion in the Communication treatment. The average winning prices in Antitrust and Leniency are somewhere between the two extreme results.

Figure 2 compares the number of bid riggers in the three treatments in which pre-play communication was allowed. It shows that subjects almost always commit bid rigging in the Communication treatment (the only exception is that only one person did not enter the chat room in the 7th round). The lines of Antitrust and Leniency appear almost overlapping, and the average number of bid riggers in each group is from 2 to 3.

The top panel in Table 3 shows the average winning prices in five-round intervals. The bottom panel of Table 3 shows the statistical differences in winning prices among all the treatments (by using a Mann-Whitney U test). It shows that there is a strong difference between Benchmark and the other three treatments (the overall comparison: z=-2.38, p=0.02 for Benchmark and Communication; z=-2.07, p=0.04 for Benchmark and Antitrust; z=-2.07, p=0.04 for Benchmark and Leniency). This confirms that when communication among bidders is possible, the market becomes collusive and the transaction prices are significantly higher than the ones in a competitive market. One interesting finding is that the difference between Benchmark and Antitrust is no longer significant in the last interval (Round 11-round 15). This means that imposing fines against bid riggers dissolves cartels eventually. On the other hand, the difference between Benchmark and Leniency is consistently significant across all the intervals. However, there is no significant difference between Antitrust and Leniency in all the intervals (the overall comparison: z=-0.15, p=0.88). The differences between Communication and Antitrust, and between Communication and Leniency are also statistically significant (the overall comparison: z=1.69, p=0.09; z=2.37, p=0.02).
respectively). They indicate that introducing an antitrust policy is effective in lowering the transaction price.

The top panel of Table 4 shows the average number of bid riggers in five-round intervals. The bottom panel of Table 4 shows the statistical differences in the number of bid riggers among all the treatments in the same way as in Table 3. Similar to the statistical results in Table 3, the difference between Communication and Antitrust and between Communication and Leniency are significant (the overall comparison: z=2.37, p=0.02, z=2.37, p=0.02, respectively). On the other hand there is no significant difference between Antitrust and Leniency (the overall comparison: z=0.29, p=0.77).

Table 5 summarizes more results on the average winning price of bid riggers and those of non bid riggers, the rate of bid rigging, and the rate of using the leniency program. The rates of bid rigging in the Antitrust and Leniency treatments are 73.3% and 66.7% respectively. The average durations of bid rigging are also similar between Antitrust and Leniency (5.5 rounds and 5.7 rounds, respectively).

One puzzling finding for the Antitrust and the Leniency treatment in Table 5 is that the average winning price among bid rigging groups is lower than the one among non bid rigging groups. This contradictory result stems from the fact that some groups had already reached collusion in the practice rounds and decided to bid the reserve price and not to enter the chat room in the real rounds. On the other hand, subjects in the groups which could not reach a collusive agreement within the practice rounds started with lower prices. We will discuss the effects of pre-play bid rigging in the following section.

### 5.2 Pre-play Collusion in the Practice Rounds and Its Effects on Bid Prices
To analyze the puzzle raised in the previous section more closely, we classified groups by their chat content in the practice rounds of both Antitrust and Leniency. We use the term “pre-collusive” for those groups that made a collusive agreement within the practice rounds, and “non pre-collusive” for those groups which could not reach any collusive agreement within the practice rounds. $ ^{19} $ $ ^{20} $ Table 6 shows that the average winning prices among pre-collusive groups are much higher than non pre-collusive groups in both Antitrust and Leniency. Moreover, we divided the data according to whether more than one person entered the chat room (categorized as “bid rigging”) or not (categorized as “non bid rigging”) in the real rounds. It shows that “non bid rigging” subjects in pre-collusive groups kept their promise of price fixing in the real rounds and the winning price of those cases are even higher than those of “bid rigging” subjects in pre-collusive groups (the average winning prices of “non bid rigging groups” in Antitrust and Leniency are 180.2 and 182.5, respectively).

Except for one group, all the groups in Antitrust agreed on the price fixing scheme in which everybody bids the reserve price every round. One group kept their collusion until the last round (i.e. the winning price of this group was always 200). One other group maintained their collusion until the 5th round. However, the collusion of this group started breaking up in the 6th round. The winning price of this group went down to 110 in the 9th round and never went up again until the last round. The other pre-collusive group discussed the same price fixing scheme in beginning of the 1st round. However, their collusion was dissolved immediately, and the winning price of this group went down to 110 in the 2nd round and it never went up again until the last round.
round. It seems difficult to keep the pre-play promise for a long time without having communication together again in the real rounds.

In the Leniency treatment, there were two groups which discussed price fixing within the practice rounds. One group maintained collusion until the 9th round, and the other maintained collusion until the 10th round. After those rounds, the groups started breaking up their collusions and ended up with winning prices of 110 or 100.

The other two groups started competitively. One of the groups went down to 110 from the beginning and never managed to reach any collusion. The other group started competitively from the first round and remained competitive until the 8th round (i.e. the winning price was 110 in all these rounds). However, all the members of this group started colluding from the 9th round. Although they did not collude until the 9th round, there were a number of people who entered the chat room who intended to form a collusion (3 subjects were in the chat room from round 1 to round 3, and 4 subjects were in the chat room from round 4 to round 8. Before the 9th round, subjects who had already entered the chat room agreed to bid 110 together by saying, “Let’s bid 110 together until the last subject enters the chat room.”) Their attempt was successful and the last subject finally entered the chat room at the 9th round. As soon as this subject joined the chat room, the group started bidding 200 together from the 9th round until 12th round. Although the winner in such a case is chosen randomly, 4 different subjects happened to win in the 9th to 12th rounds. The remaining subject who had not won in any of the rounds told about that in the chat room at the beginning of 13th round. The other members decided to make him win for sure by using another kind of price fixing.
scheme, in which one bidder bid 190 and the others bid 200. They used this price fixing scheme from the 13th round until the end. $ ^{21} $

Even if there was an agreement to repeat collusion within the practice rounds, or such collusion emerged in the middle of the real rounds, outsiders who do not enter the chat room make it difficult for insiders (bid riggers) to raise their bidding prices. $ ^{22} $

Except for one group in Leniency, there was no group which managed to start collusion within the real rounds. Table 6 shows that the average winning prices of non pre-collusive groups are not high. Although the average winning prices of bid riggers in non pre-collusive groups in Leniency seem to be relatively higher than those of non bid riggers, it is due to the exceptional group which started collusion from the 9th round described above. Table 7 compares the rate of change in the winning price between pre-collusive groups and non pre-collusive groups, and between bid riggers and non bid riggers. It shows that the price decline in pre-collusive groups is higher than non pre-collusive groups, which confirms that the pre-play collusion did not last long and was dissolved eventually. The results of all cells in Table 7 are negative except for the cell of bid riggers in non pre-collusive groups. This reflects the behavior of the group which started collusion from the 9th round.

Overall, it seems that the fine and the monitoring rate introduced in this experiment threaten individual bidders strongly enough to deter cartels both in Antitrust and Leniency. Since we do not have enough samples, we are not yet sure whether the one
emergence of collusion within the real rounds is just a rare case or whether it could happen often. Also, we are not sure whether this emergence is because the leniency program makes it easier for bid riggers to start colluding. It might be true that although leniency programs can intercept established collusions (pre-play collusions), they might be only partially effective in preventing newly generated bid rigging.

Without either bid rigging or pre-play collusion, we found that the average winning price was nearly the competitive price (109.1 and 109.3 in Antitrust and Leniency, respectively).

### 5.3 Who Used the Leniency Program?

Table 8 classifies what kind of bid riggers used the leniency programs. “Defect” means a bid rigger who cheated other bid riggers by bidding a price lower than 190. “Win” means winning an auction. 90% of “Defect and Win” bid riggers used the leniency program. The reason for this behavior is obviously to protect their profits. This observation is similar to the result in Hinloopen and Soetvent (2005). $ ^{23} $

One interesting finding is that subjects who did not win the auction also frequently applied for the leniency program. There is no incentive for them to do that for their own profit. However, they could reduce the winner’s profit if they applied for the leniency program faster than the winner. Subjects answered in the post-experiment questionnaire that they understood the experiment game before the experiment was started, so we believe that this behavior is not due to confusion.

### 5.4 Comparison of Collected Fines between Antitrust and Leniency