This paper provides a complete characterization of Pure Strategy Nash equilibria (PSNE) in an oligopoly model with power demand function recently proposed in the literature (Huang, 2004; Blavatskyy, 2018). This characterization shows that, if the marginal cost of production is strictly positive, then either there is a unique symmetric PSNE (when the demand function is sufficiently elastic) or there is no PSNE at all (when demand function is relatively inelastic). We also provide a novel interpretation of the unsatisfied demand as the demand of a social planner who partially supplies the market aiming at regulating the equilibrium price. Comparative statics results show that, if the marginal cost is zero, then the social planner can reduce the equilibrium price to zero without absorbing any additional demand. We also extend our analysis to the case when firms have different marginal costs and the elasticities of demand are firm specific. In particular, we show that the extended game has at least one PSNE when the firms’ demands are sufficiently elastic and when the unsatisfied demand is positive.

本文提供了最近在文献中提出的具有权力需求函数的寡头模型中的纯策略纳什均衡（PSNE）的完整表征（Huang，2004; Blavatskyy，2018）。该特征表明，如果边际生产成本严格为正，那么要么存在唯一的对称PSNE（当需求函数具有足够的弹性时），要么根本不存在PSNE（当需求函数相对缺乏弹性时）。我们还提供了对未满足需求的新颖解释，该需求是社会计划者的需求，该计划者部分提供了旨在调节均衡价格的市场。比较静态结果表明，如果边际成本为零，那么社会计划者可以在不吸收任何额外需求的情况下将均衡价格降至零。我们还将分析扩展到企业具有不同边际成本且需求弹性是企业特定情况的情况。特别是，我们表明，当企业的需求具有足够的弹性且需求未满足时，扩展博弈至少具有一个PSNE。