Abstract
In this paper, we analyze the dynamic-pricing decisions of differentiated products for retailers operating in a competitive environment, for a finite-time horizon, limited initial inventory, and in the presence of the reference effect. Customers learn from the past prices of retailers and form their estimate of sales prices, called the reference price effect, and use it to make a decision on choosing a retailer to make a purchase. The demand is uncertain, and the customer choice behavior is modeled based on a Multinomial Logit model, modified to incorporate the reference effect. The complexity of the problem increases under conditions of competition and demand uncertainty and cannot be analyzed using conventional methods. Therefore, we have used a neural network-based algorithm called Revenue-Based Neural Network (RBNN) to dynamically calculate the competitive price in order to increase the retailer’s revenue. We have analyzed the effect of competition and the performance of RBNN algorithm under two scenarios: a monopolistic situation in which a retailer uses the RBNN policy to maximize its revenue, and a duopolistic situation in which one retailer uses the RBNN strategy and the other uses an adaptive policy called Derivative Following (DF). The results of the experiments show that the pricing policy under duopolistic conditions highly affects the income of retailers in the presence of reference price. The RBNN policy outperforms the DF policy due to the learning process on the customers’ reference price. By charging higher prices in the RBNN strategy, the seller trades off the current revenue with the long-term revenue resulting from formation of higher levels of the reference price in customers’ minds and earns more revenue than its competitor overall.
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References
Abdallah, T., and G. Vulcano. 2021. Demand estimation under the multinomial logit model from sales transaction data. Manufacturing & Service Operations Management 23 (5): 11961–12216.
Allon, G., A. Federgruen, and M. Pierson. 2011. Price competition under multinomial logit demand functions with random coefficients. Harvard Business School.
Ben-Akiva, M.E., S.R. Lerman, and S.R. Lerman. 1994. Discrete choice analysis: theory and application to travel demand, 6th ed. Cambridge: The MIT Press.
Bishop, C.M. 1995. Neural networks for pattern recognition, 1st ed. Oxford: Oxford University Press.
Chen, M., and Z.L. Chen. 2015. Recent developments in dynamic pricing research: Multiple products, competition, and limited demand information. Production and Operations Management 24 (5): 704–731.
Chen, K., Y. Zha, L.C. Alwan, and L. Zhang. 2020. Dynamic pricing in the presence of reference price effect and consumer strategic behaviour. International Journal of Production Research 58 (2): 546–561.
Du, C., W.L. Cooper, and Z. Wang. 2016. Optimal pricing for a multinomial logit choice model with network effects. Operations Research 64 (2): 441–455.
Ghose, T.K. 2010. Dynamic pricing in electronic commerce using neural network (Master's thesis, Ottawa)
Greenleaf, E.A. 1995. The impact of reference price effects on the profitability of price promotions. Marketing Science 14 (1): 82–104.
Greenwald, A.R., J.O. Kephart, and G.J. Tesauro. 1999, November. Strategic pricebot dynamics. In Proceedings of the 1st ACM Conference on Electronic Commerce, EC ’99
Guadagni, P.M., and J.D. Little. 1983. A logit model of brand choice calibrated on scanner data. Marketing Science 2 (3): 203–238.
Hilsen, H.O.Ø. 2016. Simulating dynamic pricing algorithm performance in heterogeneous markets (Master's thesis, NTNU)
Kong, D. 2004, September. One dynamic pricing strategy in agent economy using neural network based on online learning. In IEEE/WIC/ACM International Conference on Web Intelligence, WI'04, 98–102. IEEE
Liu, Q., and D. Zhang. 2013. Dynamic pricing competition with strategic customers under vertical product differentiation. Management Science 59 (1): 84–101.
McFadden, D., and K. Train. 2000. Mixed MNL models for discrete response. Journal of Applied Econometrics 15 (5): 447–470.
Narahari, Y., C.V.L. Raju, K. Ravikumar, and S. Shah. 2005. Dynamic pricing models for electronic business. Sadhana 30: 231–256.
Newman, J.P., M.E. Ferguson, L.A. Garrow, and T.L. Jacobs. 2014. Estimation of choice-based models using sales data from a single firm. Manufacturing & Service Operations Management 16 (2): 184–197.
Popescu, I., and Y. Wu. 2007. Dynamic pricing strategies with reference effects. Operations Research 55 (3): 413–429.
Ratliff, R.M., B. Venkateshwara Rao, C.P. Narayan, and K. Yellepeddi. 2008. A multi-flight recapture heuristic for estimating unconstrained demand from airline bookings. Journal of Revenue and Pricing Management 7: 153–171.
Roh, H.J., S. Sharma, P.K. Sahu, and B. Mehran. 2018. Performance comparison of mode choice optimization algorithm with simulated discrete choice modeling. Modelling and Simulation in Engineering. https://doi.org/10.1155/2018/8169036.
Schlosser, R., and K. Richly. 2019. Dynamic pricing under competition with data-driven price anticipations and endogenous reference price effects. Journal of Revenue and Pricing Management 18: 451–464.
Shakya, S., M. Kern, G. Owusu, and C.M. Chin. 2012. Neural network demand models and evolutionary optimisers for dynamic pricing. Knowledge-Based Systems 29: 44–53.
Train, K.E. 2009. Discrete choice methods with simulation, 2nd ed. Cambridge: Cambridge University Press.
Train, K.E., D.L. McFadden, and M. Ben-Akiva. 1987. The demand for local telephone service: A fully discrete model of residential calling patterns and service choices. The RAND Journal of Economics 18: 109–123.
Vives, X. 1999. Oligopoly pricing: Old ideas and new tools. Cambridge: MIT press.
Vulcano, G., G. Van Ryzin, and W. Chaar. 2010. Om practice—choice-based revenue management: An empirical study of estimation and optimization. Manufacturing & Service Operations Management 12 (3): 371–392.
Vulcano, G., G. Van Ryzin, and R. Ratliff. 2012. Estimating primary demand for substitutable products from sales transaction data. Operations Research 60 (2): 313–334.
Winer, R.S. 1986. A reference price model of brand choice for frequently purchased products. Journal of Consumer Research 13 (2): 250–256.
Wu, S., Q. Liu, and R.Q. Zhang. 2015. The reference effects on a retailer’s dynamic pricing and inventory strategies with strategic consumers. Operations Research 63 (6): 1320–1335.
Yang, H., D. Zhang, and C. Zhang. 2017. The influence of reference effect on pricing strategies in revenue management settings. International Transactions in Operational Research 24 (4): 907–924.
Zhang, J., W.Y.K. Chiang, and L. Liang. 2014. Strategic pricing with reference effects in a competitive supply chain. Omega 44: 126–135.
Zhao, N., Q. Wang, P. Cao, and J. Wu. 2021. Pricing decisions with reference price effect and risk preference customers. International Transactions in Operational Research 28 (4): 2081–2109.
Zhao, N., Q. Wang, and J. Wu. 2022. Optimal pricing and ordering decisions with reference effect and quick replenishment policy. International Transactions in Operational Research 29 (2): 1188–1219.
Zhou, Q., Y. Yang, and S. Fu. 2022. Deep reinforcement learning approach for solving joint pricing and inventory problem with reference price effects. Expert Systems with Applications. https://doi.org/10.1016/j.eswa.2022.116564.
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Famil Alamdar, P., Seifi, A. Dynamic pricing of differentiated products under competition with reference price effects using a neural network-based approach. J Revenue Pricing Manag (2023). https://doi.org/10.1057/s41272-023-00444-8
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DOI: https://doi.org/10.1057/s41272-023-00444-8