Multiple choices generalization of (iterated) prisoner's dilemma.

Question

Does there exist a generalization of prisoner's dilemma where there are more than two options (cooperate/defect)? If so how can it be used to determine what a good strategy is; how should the player react on the action of the other player? The situation that I have in mind is that player A confesses a lesser crime of player B. Player A might not get the highest possible reward compared to fully defecting, but the loss of player B will also be smaller. This distinction does not make much sense in the case of a single instance, but I can imagine that in the case of an iterative prisoner's dilemma the degree of cooperation/retaliation in a "tit-for-tat" strategy will be different.