Price leadership in a duopoly with capacity constraints and product differentiation.

*(English)*Zbl 0774.90012This paper investigates a duopoly model with two capacity constrained firms whose products are imperfect substitutes. Demand is assumed to be linear and symmetric between the two products, and costs are assumed to be equal to zero. Competition is in prices, and rationing is efficient. The firms play a “Stackelberg” game in which one of the firms chooses its price before the other firm. The authors calculate the subgame- perfect equilibria of this game. They then identify values of the two capacities for which both firms have identical preferences with respect to the question who should move first and who should move second. They show that the relevant capacity values are those for which both firms’ capacities are “relatively large”, and “differ significantly” from each other, and that both firms would then (weakly or strictly) prefer the firm with the larger capacity to move first. The authors argue that for these capacity values one would expect a model with endogenous sequencing for moves to generate this order of moves.

The paper is presented as an extension of recent work of R. J. Deneckere and the second author [Rev. Econ. Stud. 59, No. 1, 143-162 (1992; Zbl 0751.90017)]. Deneckere and the second author consider the case in which the two firms’ products are identical. In this case, the two firms’ preferences with respect to the question who should be the leader may be identical even if their capacities do not differ significantly.

The paper is presented as an extension of recent work of R. J. Deneckere and the second author [Rev. Econ. Stud. 59, No. 1, 143-162 (1992; Zbl 0751.90017)]. Deneckere and the second author consider the case in which the two firms’ products are identical. In this case, the two firms’ preferences with respect to the question who should be the leader may be identical even if their capacities do not differ significantly.

Reviewer: T.Börgers (London)

##### MSC:

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

91B26 | Auctions, bargaining, bidding and selling, and other market models |

91A65 | Hierarchical games (including Stackelberg games) |

91A40 | Other game-theoretic models |

##### Keywords:

product differentiation; Stackelberg game; duopoly model; capacity constrained firms; subgame-perfect equilibria
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\textit{D. Furth} and \textit{D. Kovenock}, J. Econ. 57, No. 1, 1--35 (1993; Zbl 0774.90012)

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