The experiment, IMO, isn't valid. In RL tragedy of commons, the selfish don't really suffer that much .. it's usually everyone else that does.
I've had teachers offer various concepts like this over the years. One gave out simple vouchers for various points as awards for "fun" "games". I asked him if I applied ten points toward a 97/100 exam, would it cap at 100 or go to 107? He told me to sell the voucher to someone who needed it more.
Best lesson I ever got.
So, a 20 person class has 2 6pt slots. You take the bids and collect and hold the money. Grades are announced and then you hand out the money or give it back to the original bidders in case of betrayal. The spoiler is basically denying the points and cash to everyone. I get the feeling the identity of the spoiler would be found, if for no other reason all the innocent folks showing their papers. I hope the spoiler is graduating and not coming back because that type of crap is remembered.
If I were in the class I'd propose a weighted lottery where everyone had a chance to be one of the sixes but those with worse grades had a somewhat better chance. While there might be disgruntlement over the weight, I'd guess it'd be less severe than if someone that an entire fairness factor was being ignored.
An interesting questions would be what to do if someone issued an ultimatum to the group "give me one of the sixes or I will ruin it for everyone". I'd think in that case every move ends with no one getting any points.
If you think that's a safe option, you've clearly never dealt with large groups.
Actually, I'd say that increases the validity since they do it even tho they know it is more likely to have negative consequences than RL.