We study the pricing game between competing retailers under various random coefficient attraction choice models.We characterize existence conditions and structure properties of the equilibrium.Moreover,we explore how the randomness and cost parameters affect the equilibrium prices and profits under multinomial logit (MNL),multiplicative competitive interaction (MCI) and linear attraction choice models.Specifically,with bounded randomness,for the MCI and linear attraction models,the randomness always reduces the retailer's profit.However,for the MNL model,the effect of randomness depends on the product's value gap.For high-end products (i.e.,whose value gap is higher than a threshold),the randomness reduces the equilibrium profit,and vice versa.The results suggest high-end retailers in MNL markets exert more effort in disclosing their exact product performance to consumers.We also reveal the effects of randomness on retailers'pricing decisions.These results help retailers in making product performance disclosure and pricing decisions.
[1] Schön, C.:On the product line selection problem under attraction choice models of consumer behavior. Eur. J. Oper. Res. 206(1), 260-264(2010)
[2] Kamakura, W.A., Russell, G.J.:A probabilistic choice model for market segmentation and elasticity structure. J. Mark. Res. 26(4), 379-390(1989)
[3] Chintagunta, P.K., Jain, D.C., Vilcassim, N.J.:Investigating heterogeneity in brand preferences in logit models for panel data. J. Mark. Res. 28, 417-428(1991)
[4] Aksoy-Pierson, M., Allon, G., Federgruen, A.:Price competition under mixed multinomial logit demand functions. Manag. Sci. 59(8), 1817-1835(2013)
[5] Luce, R.D.:Individual Choice Behavior:A Theoretical Analysis. Wiley, New York (1959)
[6] Bell, D.E., Keeney, R.L., Little, J.D.C.:A market share theorem. J. Mark. Res. 12(2), 136-141(1975)
[7] McFadden, D., et al.:Conditional logit analysis of qualitative choice behavior. In:Zarembka, P.(ed.) Frontiers in Econometrics, pp. 105-142. Academic, London (1973)
[8] Urban, G.L.:A mathematical modeling approach to product line decisions. J. Mark. Res. 6, 40-47(1969)
[9] Hanssens, D.M., Parsons, L.J., Schultz, R.L.:Market Response Models:Econometric and Time Series Analysis, vol. 12. Springer Science&Business Media, Berlin (2003)
[10] Xie, Y., Xie, L., Lu, M., Yan, H.:Performance-price-ratio utility:market equilibrium analysis and empirical calibration studies. Prod. Oper. Manag. 30, 1442-1456(2020)
[11] Rossi, P.E., Allenby, G.M.:A Bayesian approach to estimating household parameters. J. Mark. Res. 30, 171-182(1993)
[12] Hanson, W., Martin, K.:Optimizing multinomial logit profit functions. Manag. Sci. 42(7), 992-1003(1996)
[13] Song, J.-S., Xue, Z.:Demand management and inventory control for substitutable products. SSRN Electr. J. https://doi.org/10.2139/ssrn.3866775
[14] Li, H., Huh, W.T.:Pricing multiple products with the multinomial logit and nested logit models:concavity and implications. Manuf. Serv. Oper. Manag. 13(4), 549-563(2011)
[15] Gallego, G., Wang, R.:Multiproduct price optimization and competition under the nested logit model with product-differentiated price sensitivities. Oper. Res. 62(2), 450-461(2014)
[16] Li, G., Rusmevichientong, P., Topaloglu, H.:The d-level nested logit model:assortment and price optimization problems. Oper. Res. 63(2), 325-342(2015)
[17] Alptekino? glu, A., Semple, J.H.:The exponomial choice model:a new alternative for assortment and price optimization. Oper. Res. 64(1), 79-93(2016)
[18] Huh, W.T., Li, H.:Pricing under the nested attraction model with a multistage choice structure. Oper. Res. 63(4), 840-850(2015)
[19] Gallego, G., Ratliff, R., Shebalov, S.:A general attraction model and sales-based linear program for network revenue management under customer choice. Oper. Res. 63(1), 212-232(2015)
[20] Topkis, D.M.:Equilibrium points in nonzero-sum n-person submodular games. SIAM J. Control. Optim. 17(6), 773-787(1979)
[21] Vives, X.:Oligopoly Pricing:Old Ideas and New Tools. MIT Press, Cambridge (2001)
[22] Mizuno, T.:On the existence of a unique price equilibrium for models of product differentiation. Int. J. Ind. Organ. 21(6), 761-793(2003)
[23] Caplin, A.:Aggregation and imperfect competition:on the existence of equilibrium. Econom. J. Econom. Soc. 59, 25-59(1991)
[24] Gallego, G., Huh, W.T., Kang, W., Phillips, R.:Price competition with the attraction demand model:existence of unique equilibrium and its stability. Manuf. Serv. Oper. Manag. 8(4), 359-375(2006)
[25] Yang, L., Guo, P., Wang, Y.:Service pricing with loss-averse customers. Oper. Res. 66(3), 761-777(2018)
[26] Federgruen, A., Ming, H.:Sequential multiproduct price competition in supply chain networks. Oper. Res. 64(1), 135-149(2016)
[27] Wang, R.:What is the impact of nonrandomness on random choice models?Manuf. Serv. Oper. Manag.(2021)
[28] Debreu, G.:A social equilibrium existence theorem. Proc. Natl. Acad. Sci. 38(10), 886-893(1952)
[29] Fan, K.:Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. 38(2), 121-126(1952)
[30] Glicksberg, I.L.:A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Am. Math. Soc. 3(1), 170-174(1952)
[31] Bensoussan, A., Xie, Y., Yan, H.:Joint inventory-pricing optimization with general demands:an alternative approach for concavity preservation. Prod. Oper. Manag. 28(9), 2390-2404(2019)
