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.
The notion of reference price is becoming more popular in modelling price effects on consumers' purchasing behaviour. In order to understand the formation of reference price, an integrative analysis of the different concepts of reference price is proposed here. We present a classification of some twenty-six different concepts of reference price, based on an analysis of the different cognitive processes involved in the different conceptualisations. In addition, similarities and differences between the different concepts are examined. Finally, we consider utilization of particular reference price concepts in reference price modelling as well as in managerial decisions pertinent to various market situations.
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