Explicit Solutions of Optimization Models and Differential Games with Nonsmooth (Asymmetric) Reference-Price Effects

Gadi Fibich (), Arieh Gavious () and Oded Lowengart ()
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Gadi Fibich: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Oded Lowengart: School of Management, Ben-Gurion University, Beer-Sheva 84105, Israel

Operations Research, 2003, vol. 51, issue 5, 721-734

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.

Keywords: Marketing; pricing:optimal pricing with reference effects; Games; differential:nonsmooth differential games; Optimal control; applications: nonsmooth problems (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (69)

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