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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 planningdoi:10.1287/opre.51.5.721.16758 fatcat:lhrrjthj4bfylo6xacaaxs7khu