In a two-stage repeated classical game of prisoners' dilemma the knowledge
that both players will defect in the second stage makes the players to defect
in the first stage as well. We find a quantum version of this repeated game
where the players decide to cooperate in the first stage while knowing that
both will defect in the second.Comment: Revised in the light of referee's comments. Latex, 10 pages, 1 eps
figure, submitted to Physics Letters