The main structure of our system, is that we have owners who define labs with problems and prices to win. Each lab has participants who debate each other about the problem of the lab. In order to be good in the debates you must have a good solution to the problem. The best debaters have the best solutions to the problem and will win the prize.
The side-choosing games take place during the debates in a lab. Each lab is based on an extensive form game, without ties. We choose a legal position p as the start position.
If the debaters choose opposite sides, we play the extensive form game from position p and determine the winner and loser. The outcome for two debaters x and y will be one of the following rows. W is the winner column and L is the loser column.
W L Forced x y none y x noneIf both debaters choose the same side, we play two extensive form games from p, introducing the notion of a forced debater or of a devil's advocate. The first game has x forced and the outcome will be one of the following rows.
W L Forced x y x y x xThe second game has y forced and the outcome will be one of the following rows.
W L Forced x y y y x y
Because money is at stake it is important that we care for guaranteed collusion resilience. Collusion is when a debater, who is not in control, has his ranking changed behind his back. This can happen when debaters lose (although they could win) to help their colluding friends. The concept of forced debaters is crucial for defining and enforcing collusion resilience.
For more details: Side-Choosing Games
Karl Lieberherr, March, 2014