Article ID: | iaor20041497 |
Country: | United States |
Volume: | 51 |
Issue: | 5 |
Start Page Number: | 721 |
End Page Number: | 734 |
Publication Date: | Sep 2003 |
Journal: | Operations Research |
Authors: | Gavious Arieh, Fibich Gadi, Lowengart Oded |
Keywords: | game theory |
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.