Working paper

Cooperation in the Presence of an Advantaged Outsider

Guillaume Cheikbossian, and Philippe Mahenc


This paper analyzes how the stability of the tacit cooperation within a fringe of sev- eral identical ?rms is affected by the presence of a more e¢ cient ?rm which does not take part in their cooperative agreement. The model assumes that the ?rms of the fringe adopt ?stick and carrot?strategies à la Abreu (1986, 1988) to support cooperation, while the outside ?rm plays its one-period best response function to these strategies, regardless of the history of play. Assuming a linear demand function and constant marginal costs, we then obtain conditions for the coopera- tion within the fringe to be sustainable and focus on the most cooperative symmetric punishment (MCSP) that sustains cooperation. We show that the MCSP is harsher when the number of ?rms involved in the agreement is relatively large or when their relative cost disadvantage is relatively small. However, both a larger number of ?rms and a larger cost disadvantage make it more di¢ cult to sustain the cooperation.


Repeated Game; Tacit Collusion; Optimal Punishments; Cost Asymmetry; Outsider;

JEL codes

  • C73: Stochastic and Dynamic Games • Evolutionary Games • Repeated Games
  • D43: Oligopoly and Other Forms of Market Imperfection
  • L13: Oligopoly and Other Imperfect Markets

See also

Published in

TSE Working Paper, n. 13-390, August 2012