es. The repetition for a predetermined finite number of plays does nothing to help them in achieving a collusive outcome. This happens because, though each player actually plays forward in sequence from the first to the last round of the game, that player needs to consider the implications of each round up to and including the last, before making its first move. While choosing its strategy it's sensible for every firm to start by taking the final round into consideration and then work backwards. As we realise the backward induction, it becomes evident that the fifth and the final round of the game would be absolutely identical to a "one-shot" game and, thus, would lead to exactly the same outcome. Both firms would cheat on the agreement at the final round. But at the start of the fourth round, each firm would find it profitable to cheat in this round as well. It would gain nothing from establishing a reputation for not cheating if it knew that both it and its rival were bound to cheat next time. And this crucial fact of inevitable cheating in the final round undermines any alternative strategy, e.g. building a reputation for not cheating as the basis for establishing the collusion. Thus cheating remains the dominant strategy. * NOTE: the is however one assumption about slightly incomplete information, which allows collusive outcome to occur in the finitely repeated game, but I will left it for the discussion some paragraphs later.c.)_ Infinite game case. Now lets consider the infinitely repeated version of the game. In this kind of game there is always a next time in which a rival's behaviour can be influenced by what happens this time. In such a game, solutions to the problems represented by the prisoners dilemma are feasible. i.) "Trigger" strategy Suppose that firms discount the future at some rate "w", where "w" is a number between O and 1. That is, players attach weight "w" to what happens next period. Provided that "w" is not ...
