Collusive price rigidity under price-matching punishments

► We analyse an infinitely repeated game of the rivalry of the kinked demand curve. ► The best collusive prices can be rigid over time despite small cost changes. ► The price is between the low-cost monopoly price and the high-cost Nash price. ► The present discounted values of profits are decreasing in the level of high costs. ► Price rigidity depends on firm numbers, differentiation and high-cost phase duration.