Duopoly information equilibrium: Cournot and Bertrand.

*(English)*Zbl 0546.90011In a symmetric differentiated duopoly model, where firms have the same private information about an uncertain linear demand, a two-stage game is considered. In this game, the firms first decide how much of their private information to put in the common pool, and then choose an action (quantity or price) for each ”signal” they may receive, so that in this second stage a Bayesian (Cournot or Bertrand competition respectively) game is played.

The present paper states that, under certain assumptions, the preceding two-stage game has a unique subgame perfect equilibrium in dominant strategies at the fist stage. With substitutes this subgame suggests no pooling of information in Cournot competition and complete pooling in Bertrand competition, whereas with complements the result is reversed.

Then, the author analyzes the two extreme situations, complete sharing of information and no sharing, in welfare terms (more precisely in terms of the expected consumer surplus and the expected total surplus), and he concludes that: if the goods are substitutes the outcome of the two-stage game is never optimal with respect to information sharing in Cournot competition, and it may be optimal in Bertrand competition if the goods are close to perfect substitutes, whereas if the goods are complements the outcome is always optimal with respect to information sharing in both, Cournot and Bertrand competitions.

Finally, it is emphasized that just as Bertrand competition is more efficient than Cournot competition in the certainty models, so in the uncertainty model with incomplete information Bertrand competition is more efficient than Cournot competition. Moreover, the social value of information is positive in Cournot and negative in Bertrand competition, whereas the private value of information is positive in both competitions, although it is larger in Cournot than in Bertrand competition if the goods are substitutes and with complements the result is reversed.

The present paper states that, under certain assumptions, the preceding two-stage game has a unique subgame perfect equilibrium in dominant strategies at the fist stage. With substitutes this subgame suggests no pooling of information in Cournot competition and complete pooling in Bertrand competition, whereas with complements the result is reversed.

Then, the author analyzes the two extreme situations, complete sharing of information and no sharing, in welfare terms (more precisely in terms of the expected consumer surplus and the expected total surplus), and he concludes that: if the goods are substitutes the outcome of the two-stage game is never optimal with respect to information sharing in Cournot competition, and it may be optimal in Bertrand competition if the goods are close to perfect substitutes, whereas if the goods are complements the outcome is always optimal with respect to information sharing in both, Cournot and Bertrand competitions.

Finally, it is emphasized that just as Bertrand competition is more efficient than Cournot competition in the certainty models, so in the uncertainty model with incomplete information Bertrand competition is more efficient than Cournot competition. Moreover, the social value of information is positive in Cournot and negative in Bertrand competition, whereas the private value of information is positive in both competitions, although it is larger in Cournot than in Bertrand competition if the goods are substitutes and with complements the result is reversed.

Reviewer: M.A.Gil Alvarez

##### MSC:

91B24 | Microeconomic theory (price theory and economic markets) |

91A40 | Other game-theoretic models |

91A80 | Applications of game theory |

91A20 | Multistage and repeated games |

##### Keywords:

symmetric differentiated duopoly model; uncertain linear demand; two- stage game; private information; subgame perfect equilibrium; Cournot competition; Bertrand competition; social value of information; private value of information
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##### References:

[1] | Basar, T; Ho, V.C, Informational properties of the Nash solutions of two stochastic nonzero-sum games, J. econom. theory, 7, 370-387, (1976) |

[2] | Clarke, R, Collusion and the incentives for information sharing, () |

[3] | Crawford, V; Sobel, J, Strategic information transmission, Econometrica, 50, 1431-1451, (1982) · Zbl 0494.94007 |

[4] | Dixit, A.K, A model of duopoly suggesting a theory of entry barriers, Bell J. econom., 10, 20-32, (1979) |

[5] | Gal-Or, E, Information sharing in oligopoly, (1982), University of Pittsburgh, working paper · Zbl 0578.90008 |

[6] | Harris, R; Lewis, T, Strategic commitment under uncertainty with private information, (1982), California Institute of Technology, working paper |

[7] | Harsanyi, J; Harsanyi, J; Harsanyi, J, Games with incomplete information played by Bayesian players, III, Management sci., Management sci., Management sci., 14, 486-502, (1967-1978) · Zbl 0177.48501 |

[8] | Leland, H, Theory of the firm facing uncertain demand, Amer. econom. rev., 62, 278-291, (1972) |

[9] | Milgrom, P; Weber, R, A theory of auctions and competitive bidding, Econometrica, 50, 1089-1122, (1982) · Zbl 0487.90017 |

[10] | Milgrom, P; Weber, R, The value of information in a sealed bid auction, J. math. econom., 10, 105-114, (1982) · Zbl 0481.90052 |

[11] | Novshek, W; Sonnenschein, H, Fulfilled expectations Cournot duopoly with information acquisition and release, Bell J. econom., 13, 214-218, (1982) |

[12] | Selten, R, Re-examination of the perfectness concept for equilibrium points of extensive games, Internat. J. game theory, 5, 25-55, (1975) · Zbl 0312.90072 |

[13] | Singh, N; Vives, X, Price and quantity competition in a differentiated duopoly, () |

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