| Abstract: | Empirical evidence, and theoretical results have shown that, in an industry, higher concentration index indicates higher price‐cost margin. In order to detect collusive behaviour the antitrust authorities often monitor the Herfindahl‐Hirschman Index. We consider N‐firm oligopolies where a group of firms partially cooperate with each other, and monitor the Herfindahl‐Hirschman Index as well. After suspecting that the authorities might notice the violation of antitrust regulations, they stop their cooperation. The group will not cooperate again until the Index moves back to the legal domain. This flip‐flop dynamical model is formulated, the equilibria are determined, and the asymptotic properties of the system are examined. |
