Prisoner’s Dilemma :: A Variation

from Alain Badiou, Lacan Anti-philosophy 3, page 244: “Lacan presents it [i.e., the prisoner’s dilemma] as a ‘logical problem,’ in which a prison warden summons three prisoners and asks them to undergo a test, which will result in one of them being set free. The warden has five disks, three white and two black; he attaches one disk to the back of each prisoner, so that each can see what color disk the others have but not his own. The first prisoner who correctly deduces the color of his disk will be released.” Badiou does not give the answer.

This is a variation on the classical Prisoners’ Dilemma. In this case, …

If the warden distributes the disks B – B – W, Prisoner White will immediately know the answer; game over; so the warden will make a different distribution..

If not, the pattern will be either B – W – W or W – W – W.

B – B – B is impossible, ex hypothesi.

If the pattern is B – W – W, each prisoner will see either B – W or W – W. Since we’ve now ruled out any pattern containing B – B, if a prisoner sees a B, he knows he’s a W.

If not, the only remaining eligible pattern is W – W – W, and the prisoner who first announces that he’s a W, wins.

Black just can’t catch a break.