动态Bertrand寡头垄断

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摘要翻译：
我们研究连续时间Bertrand寡头垄断，在这种寡头垄断中，少数生产类似产品的公司通过设定价格相互竞争。我们首先分析这个游戏的一个静态版本，以便更好地理解在动态设置中玩的策略。在静态博弈中，我们刻画了当存在具有异质成本的$N$博弈者时的纳什均衡。在市场需求不确定的动态博弈中，不同规模的企业具有不同的生存能力，这些能力随着时间的推移而耗尽。在线性需求函数的情况下，建立了非零和随机微分对策及其关联的HJB偏微分方程组。在小竞争极限下，我们用渐近逼近刻画了该对策的某些定性特征。利用数值解进一步研究了博弈的均衡。我们发现，当一个市场是由许多相对规模相同的公司生产高度可替代商品时，消费者受益最大。然而，很大程度的可替代性并不总是导致价格的大幅下降，例如当两家公司的规模有很大差异时。
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英文标题：
《Dynamic Bertrand Oligopoly》
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作者：
Andrew Ledvina and Ronnie Sircar
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  We study continuous time Bertrand oligopolies in which a small number of firms producing similar goods compete with one another by setting prices. We first analyze a static version of this game in order to better understand the strategies played in the dynamic setting. Within the static game, we characterize the Nash equilibrium when there are $N$ players with heterogeneous costs. In the dynamic game with uncertain market demand, firms of different sizes have different lifetime capacities which deplete over time according to the market demand for their good. We setup the nonzero-sum stochastic differential game and its associated system of HJB partial differential equations in the case of linear demand functions. We characterize certain qualitative features of the game using an asymptotic approximation in the limit of small competition. The equilibrium of the game is further studied using numerical solutions. We find that consumers benefit the most when a market is structured with many firms of the same relative size producing highly substitutable goods. However, a large degree of substitutability does not always lead to large drops in price, for example when two firms have a large difference in their size.
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PDF链接：
https://arxiv.org/pdf/1004.1726

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关键词：bertrand Bertran 寡头垄断 rand ert static Bertrand 寡头 goods different