Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects
成果类型：
Article
署名作者：
Fibich, G; Gavious, A; Lowengart, O
署名单位：
Tel Aviv University; Ben-Gurion University of the Negev; Ben-Gurion University of the Negev
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.51.5.721.16758
发表日期：
2003
页码：
721-734
关键词：
摘要：
Models in marketing with asymmetric reference effects lead to nonsmooth optimization problems and differential games which cannot be solved using standard methods. In this study, we introduce a new method for calculating explicitly optimal strategies, open-loop equilibria, and closed-loop equilibria of such nonsmooth problems. Application of this method to the case of asymmetric reference-price effects with loss-aversive consumers leads to the following conclusions: (1) When the planning horizon is infinite, after an introductory stage the optimal price stabilizes at a steady-state price, which is slightly below the optimal price in the absence of reference-price effects. (2) The optimal strategy is the same as in the symmetric case, but with the loss parameter determined by the initial reference-price. (3) Competition does not change the qualitative behavior of the optimal strategy. (4) Adopting an appropriate constant-price strategy results in a minute decline in profits.