Folk theorems in a class of additively separable games

We study a class of games featuring payoff functions 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. •We study a class of games featuring additively separable payoffs.•Best replies being orthogonal, Nash equilibria are in dominant strategies.•The requirement for collusive stability is independent of the number of players.•This is independent of the punishment used.•We outline examples from economic theory and international relations.