Abstract
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.
Original language | English |
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Pages (from-to) | 721-734 |
Number of pages | 14 |
Journal | Operations Research |
Volume | 51 |
Issue number | 5 |
DOIs | |
State | Published - 1 Sep 2003 |
Keywords
- Games, differential: nonsmooth differential games
- Marketing, pricing: optimal pricing with reference effects
- Optimal control applications: nonsmooth problems
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research