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Collusive Price Rigidity Under Price Matching Punishment

In this paper we provide game theoretic support for the results of the kinked demand curve. By analyzing an infinitely repeated game where unit costs fluctuate stochastically between a low and a high state over time and where firms follow a price-matching punishment strategy, we demonstrate that price rigidity can occur in the best collusive subgame perfect Nash equilibrium for small fluctuations in costs. The critical level of high costs under which the best collusive prices are rigid is shown to depend upon the expected duration of a sequence of high-cost periods, the number of firms in the market, and the degree of product differentiation.