General description

There is a certain informational asymmetry: a person who could punish anon-collaborator can't directly observe his actions. So he has to rely on collaboration with those who have an information about the wrongdoer. Those who have an option to detect and inform the punishing authority about who commit the crime are called the whistleblowers later in the text.
When the central authority faces the such an issue with detection it can be interested in boosting the propensity of other members in the ingroup team (a team to which the perpetrator belongs to), to blow the whistle.
One of the possible solutions is to punish a random member of a group if no one detects the wrongdoer. This can be counted as collective sanctions (CS) where everyone in the group is punished by the 1/n-th of the total amount of punishment, where n is the size of the group. 
There are several different considerations that can take place and affect the efficiency of this measure.
  1. The risk of being punished for non-whistleblowing if no one informs on the perpetrator decreases the opportunity cost of whistleblowing. Thus the introduction of CS will increase the frequency of whistleblowing.
  2. The external authority may be unwilling to implement the random punishment if it does not observe who is guilty in the wrongdoing. Such a low propensity to use the CS will decrease the chance that the wrongdoer will be punished. If other members of the team would realize that the authority won't use its power to punish them for the silence they will abstain from blowing the whistle.

More specific design description

In its core there is a standard PGG with four players. 
  1. The perpetrator: he is defined here as the The Least Contributor (TLC). A participant with the smallest contribution to a collective investment is chosen. If there are more than one smallest contributors in a group, the TLC is chosen randomly from them.
  2. Sanctioning authority: a random member from the group of non-perpetrators. If the TLC is detected  (by other members of the group) he is able to apply a continuous (as in \citet{Nikiforakis_2005}) punishment which is costly for him.
  3. Ingroup members: the rest of the group apart from the perpetrator and a sanctioning authority.  They make a binary decision about detection of the TLC. This decision is costly. If no one from the ingroup members take the decision to detect and inform the sanctioning authority about the identity of the TLC he cannot be directly punished by the sanctioning authority. If no whistleblowing takes place the rest depends on the specific treatment.  Under Individual Sanctions (IS) the sanctioning authority can not further proceed with the punishment and the game ends. Under Collective Sanctions (CS)  the sanctioning authority can choose either to skip the punishment or to punish a random member of the group.
In order to collect as many data points as possible I use in this design the strategy method in role assignment.
The participants take the following decisions in order listed below:
  1. A participant takes the binary decision as if he is chosen as an ingroup member: whether he will detect the TLC so that the sanctioning authority  or not.
  2. A participant takes the continuous decision as if he is chosen as a sanctioning authority: whether he will punish the detected TLC (in case he will receive any information from the rest of the group) and by how much he will punish him, i.e. how many deduction tokens will be send to the TLC out of the additional endowment provided for punishment. Under CS treatment he also decides what will be his actions in case of no ingroup members report the TLC to him: punish or not punish the random player. 
  3. The investment decision for the public good project is made.
I invert the flow of decisions, such that the investment decision is made at the last moment while in a direct play the participants would take the investment decision first, because it does not make sense to ask for their opinion regarding the detection of TLC when they have been already asked about their contributions, and they have already made a decision to contribute nothing. 
When the group has these three decisions, I randomly pick one player from the smallest contributors. In case of full contribution of the entire group, that is when everyone invest his entire endowment to the public good, no decisions taken at stages (1) and (2) are applied. 
After the TLC is chosen, I apply the random decision of stage (2) conditional on the decision of the ingroup members who have not been chosen as the perpetrator or the sanctioning authority. That is, if all the ingroup members take the decision not to inform the sanctioning authority, no punishment is applied. If at least one has made the decision to inform then the punishment is applied on the TLC. Under CS treatment if the sanctioning authority has taken the decision to punish the random members, then he is picked randomly from the rest of the group (any member of the group with an exception of the sanctioning authority) and the punishment is applied.