A two-stage multi-period negotiation model with reference price effect

In this article, we consider the revenue management problem of firms with customers who use historical pricing data to make their purchasing decision. This behavior is modeled using the concept of reference price, which quantifies customers’ perceived ‘fair value’ of a product. We consider a segmented market consisting of two types of customers. One segment uses all price history to form a reference point and the other only uses the current price to do so. We study the revenue maximization problem of a firm who offers a two-price scheme in this market and derive closed form analytical solutions. Finally, we extend the monopoly model to a duopoly setting, and provide a numerical analysis on the added value of offering a two-price scheme compared to a single-price scheme and suggest a novel interpretation of such segmentation regime.

[1]  Manohar U. Kalwani,et al.  A Price Expectations Model of Customer Brand Choice , 1990 .

[2]  Ioana Popescu,et al.  Dynamic Pricing Strategies with Reference Effects , 2007, Oper. Res..

[3]  George T. Gilber.  Positive definite matrices and Sylvester's criterion , 1991 .

[4]  P. Kopalle,et al.  Asymmetric Reference Price Effects and Dynamic Pricing Policies , 1996 .

[5]  Chia-Wei Kuo,et al.  Dynamic Pricing of Limited Inventories When Customers Negotiate , 2011, Oper. Res..

[6]  Peter R. Dickson,et al.  Consumer Normal Price Estimation: Market versus Personal Standards , 1991 .

[7]  A. Tversky,et al.  Loss Aversion in Riskless Choice: A Reference-Dependent Model , 1991 .

[8]  Marc Nerlove,et al.  Adaptive Expectations and Cobweb Phenomena , 1958 .

[9]  R. Zeckhauser,et al.  Optimal Selling Strategies: When to Haggle, When to Hold Firm , 1983 .

[10]  R. Winer,et al.  A dynamic model of reference price and expected quality , 1996 .

[11]  William Samuelson,et al.  Status quo bias in decision making , 1988 .

[12]  Pinar Keskinocak,et al.  Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions , 2003, IEEE Engineering Management Review.

[13]  E. Greenleaf.  The Impact of Reference Price Effects on the Profitability of Price Promotions , 1995 .

[14]  Russell S. Winer,et al.  Technical Note---A Price Vector Model of Demand for Consumer Durables: Preliminary Developments , 1985 .

[15]  Lakshman Krishnamurthi,et al.  Asymmetric Response to Price in Consumer Brand Choice and Purchase Quantity Decisions , 1992 .

[16]  Lakshman Krishnamurthi,et al.  A comparative analysis of reference price models , 1997 .

[17]  Gadi Fibich,et al.  Explicit Solutions of Optimization Models and Differential Games with Nonsmooth (Asymmetric) Reference-Price Effects , 2003, Oper. Res..

[18]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[19]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[20]  Ruqu Wang.  Bargaining versus posted-price selling , 1995 .

[21]  D. Putler.  Incorporating Reference Price Effects into a Theory of Consumer Choice , 1992 .

[22]  Russell S. Winer,et al.  A reference price model of brand choice for frequently purchased products. , 1986 .

[23]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[24]  Preyas S. Desai,et al.  Let Me Talk to My Manager: Haggling in a Competitive Environment , 2004 .

[25]  Bruce G. S. Hardie,et al.  Modeling Loss Aversion and Reference Dependence Effects on Brand Choice , 1993 .

[26]  G. Tellis,et al.  Contextual and Temporal Components of Reference Price , 1994 .