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

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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 languageEnglish
Pages (from-to)721-734
Number of pages14
JournalOperations Research
Volume51
Issue number5
DOIs
StatePublished - 1 Sep 2003

Keywords

  • Games, differential: nonsmooth differential games
  • Marketing, pricing: optimal pricing with reference effects
  • Optimal control applications: nonsmooth problems

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