Punishment paths and cartel size

Using a 'Dominant-group-fringe' model, we show that the choice of a subgame perfect Nash equilibrium (SPNE) punishment path in the event that unilateral defection occurs depends upon the common discount parameter, and that when the discount parameter is given the punishment path may depend upon the size of the dominant group. The choice of punishment path is thus endogenous. A striking result is that only for sufficiently small dominant groups in sufficiently small industries are there cases where costs affect these choices. Consequently, costs are irrelevant to the choice of punishment in industries with a large number of firms.