This paper proposes a competitive pricing model based on perceived price, using multinominal logit model (MNL) as a consumer response function and applying non-cooperative game for the behavior of firms. To explain perceived price, many concepts such as reference price and reservation price have been suggested in consumer research. MNL was applied in order to describe consumer choice under these concepts. However, in the literature of competitive strategy, MNL was employed with the assumption that utility function is linear with respect to price. Under this linearity assumption, it is difficult to deal with perceived price except when it is explained by the above two concepts.In this paper, we relax this assumption to capture perceived price. This makes our model adaptable to wide variations of perceived price. We assume that the utility function consists of components of perceived price and perceived attribute. In the case of non-linear utility function, profit of competing firms or equivalent payoff function in game theoretic terminology is no longer assured to be quasi-concave. Moreover, we do not set the upper limit for product price. Therefore, the Nash equilibrium may not be unique in pure strategy. If Nash equilibrium does not exist, some researches have resorted to mixed strategy, which implies randomized price. If multiple equilibria exist, there is a possibility that equilibrium price changes from one to the other. In both cases, the market is unstable. First, we assume a multiplicity of Nash equilibria under a pure strategy. We conduct comparative statics of local equilibria that locally satisfy the conditions of Nash equilibrium. This analysis reveals the monotonicity of price, market share, and profit in local equilibria with respect to a perceived product attribute. Second, we focus on a two-firm game. We analyze the behavior of local best-reply function, which denotes the local optimum in a pure strategy when the strategy of the other firm is given. As a result of this analysis, we specify the conditions for the uniqueness of the Nash equilibrium. Third, we conducted a small numerical experiment of our model in the market of recreational vehicles. When the utility function is a quadratic function with respect to price, our model shows an outcome similar to the linear utility models. When the utility function is a cubic function with respect to price, our model shows an outcome quite different from the linear utility models, We conclude that curvature of the utility function with respect to price plays an important role in determining the uniqueness of Nash equilibrium and the marketing strategy of firms.
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