This is interesting.
If you are lazy to click, this economy professor experimented on his students every year. He will get 8 students to bid on a $20 bill. The highest bidder gets it, paying whatever he or she bid. Equal bidders split the loot. Bidders may collude, but must bid individually and in sealed secret.
The game is easy enough: lie to others on a collusion deal and break rank to bid just a bit higher to win. Clearly, for this year, 7 students bid 1 cent — with the plan to split the money 8 ways. But one of them broke rank and bid 5 cents, pocketing $19.95 entirely.
What about creditability? If this is a one-time deal, the cheater walked away smart and profitable. But if this is a long-term relationship, she just earned the reputation of someone who cannot be trusted. As long as she is one of the players, others will assume that she will cheat and therefore not even try to collude.
I am pretty sure that game theorists have an optimizing strategy for this scenario. To me, the algorithm is quite simple.
- I would propose everyone to bid 1 cent. At the same time, everyone needs to put up with a collateral. Since the loot for cheating will be nearly $20, that will be the collateral.
- If no one cheats, everyone gets their collateral back and split the win.
- If someone cheats, say by bidding 2 cents. The cheater will get $19.98, but lose the collateral. The other 7 people will split it equally. The cheater loses 2 cents and others win $2.85 each.
I guess there can be the optimal collateral size to make it revenue neutral. But you got the idea.