Infinite horizon oligopoly with asynchronous moves: Cournot-Bertrand reversal

Abstract

In an infinite-horizon oligopoly game, if moves are not synchronised across firms, sustainability of tacitly collusive equilibria becomes substantially distinct from that in a classical simultaneous-move supergame. In linear duopoly, the critical discount factor becomes higher in Bertrand than in Cournot, yet for a low discount factor with which collusion is unsustainable the equilibrium discounted streams of non-collusive profits are higher in a Bertrand game than in a Cournot game. These features are contrary to the well-known observation in synchronous-move supergames, reflecting the tendency that once a deviation path is initiated, then an asynchronous-move Cournot game converges to a competitive outcome more quickly than an asynchronous-move Bertrand game.

Keywords:

• Collusion
• trigger strategy
• -best response
• convergence
• static deviation
• foresighted deviation

Acknowledgements

The author should like to thank Jeff Kline for his insightful comments on an earlier draft of this paper. Also special thanks to participants of the University of Tokyo and National Taiwan University Joint Conference on Industrial Organization (2015) for helpful comments and suggestions. Toshihiro Matsumura, and two anonymous referees for the Asia Pacific Journal of Accounting and Economics, have most kindly offered invaluable advice, without which this work would not have materialised. The author maintains the sole responsibility for any remaining imperfections.

Notes

No potential conflict of interest was reported by the authors.