{"title":"Bertrand-Edgeworth Duopoly: Multi-Market","authors":"Jun Wang","doi":"10.2139/ssrn.3304415","DOIUrl":null,"url":null,"abstract":"Nowadays most firms compete for multiple separate markets as opposed to a single market. Extant IO works mainly focus on these firms' cooperative behavior, assuming away their capacity constraints and studying the effect of potential multi-market retaliation upon these firms' collusive incentive. With the assumption that the firms have a single capacity constraint, which applies to the multiple separate markets they compete for, this paper sheds light on the effects of the capacity constraint and demand linkages across different markets in the context of a non-cooperative duopoly model. Different from the classical single market capacity-constrained price competition theory, which has three regions divided by three different types of price equilibria as we adjust the firms' capacity constraints, two asymmetric markets capacity-constrained price competition has five regions divided by five different types of price equilibria as we adjust the firms' capacity constraints. An interesting result is that the firms do not always set higher price in the big or rich market than the small or poor market. When the capacities are endogenously determined, we find that the classical single market result (Kreps and Scheinkman 1983) that the Cournot-Nash quantity is a subgame perfect Nash equilibrium cannot hold for the two asymmetric markets competition model. In sum, the results of the asymmetric markets capacity-constrained price competition may yield different implications on merger, price leadership, and collusive behavior.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERN: Other Game Theory & Bargaining Theory (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3304415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Nowadays most firms compete for multiple separate markets as opposed to a single market. Extant IO works mainly focus on these firms' cooperative behavior, assuming away their capacity constraints and studying the effect of potential multi-market retaliation upon these firms' collusive incentive. With the assumption that the firms have a single capacity constraint, which applies to the multiple separate markets they compete for, this paper sheds light on the effects of the capacity constraint and demand linkages across different markets in the context of a non-cooperative duopoly model. Different from the classical single market capacity-constrained price competition theory, which has three regions divided by three different types of price equilibria as we adjust the firms' capacity constraints, two asymmetric markets capacity-constrained price competition has five regions divided by five different types of price equilibria as we adjust the firms' capacity constraints. An interesting result is that the firms do not always set higher price in the big or rich market than the small or poor market. When the capacities are endogenously determined, we find that the classical single market result (Kreps and Scheinkman 1983) that the Cournot-Nash quantity is a subgame perfect Nash equilibrium cannot hold for the two asymmetric markets competition model. In sum, the results of the asymmetric markets capacity-constrained price competition may yield different implications on merger, price leadership, and collusive behavior.
现在大多数公司都在多个独立的市场竞争,而不是单一的市场。现有的IO研究主要关注企业的合作行为,假设企业的产能约束,研究潜在的多市场报复对企业合谋激励的影响。假设企业在竞争的多个独立市场中存在单一的产能约束,本文揭示了在非合作双寡头模型的背景下,产能约束和需求联系对不同市场的影响。与传统的单一市场产能约束价格竞争理论不同的是,当我们调整企业的产能约束时,三个区域被三种不同类型的价格均衡所划分,而两个非对称市场的产能约束价格竞争在调整企业的产能约束时,有五个区域被五种不同类型的价格均衡所划分。一个有趣的结果是,公司并不总是在大市场或富裕市场设定比小市场或贫穷市场更高的价格。当产能是内生决定时,我们发现经典单一市场结果(Kreps and Scheinkman 1983)关于库尔诺-纳什量是子博弈的完全纳什均衡的结论在两个不对称市场竞争模型中不成立。综上所述,不对称市场的价格竞争可能对并购、价格领导和共谋行为产生不同的影响。