We study a class of games featuring payoff functions being parabolic cylinders where best reply functions are orthogonal and therefore the pure-strategy non-cooperative solution is attained as a Nash equilibrium in dominant strategies. We prove that the resulting threshold of the discount factor above which implicit collusion on the Pareto frontier is stable in the infinite supergames is independent of the number of players. This holds irrespective of whether punishment is based on infinite Nash reversion or one-shot stick-and-carrot strategy. We outline two examples stemming from economic theory and one from international relations.