Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects

Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects

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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: , ,
Keywords: game theory
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.

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