The Complex Dynamics of Bertrand-Stackelberg Pricing Models in a Risk-Averse Supply Chain

We construct dynamic Bertrand-Stackelberg pricing models including two manufacturers and a common retailer in a risk-averse supply chain with the uncertain demand. The risk-averse supply chain follows these strategies: Bertrand game between the two manufacturers and Stackelberg game between the manufacturer and the retailer. We study the effect of the price adjustment speed, the risk preference, and the uncertain demand on the stability of the risk-averse supply chain using bifurcation, power spectrum, attractor, and so forth. It is observed that there exists slip bifurcation when the price adjustment speed across some critical value, the stable region, and total profit of the risk-averse supply chain will increase with increase of and decrease with increase of . The profit of the supply chain and the two manufacturers will decrease and the weaker (retailer) is a beneficiary when the supply chain is in chaos. The fluctuation in the supply chain can be gradually controlled by the control of the price adjustment speed.

[1]  Michael R. Walls,et al.  Combining decision analysis and portfolio management to improve project selection in the exploration and production firm , 2004 .

[2]  Charles A. Holloway Decision Making Under Uncertainty: Models and Choices , 1979 .

[3]  Yang Jun Supply Chain Coordination Model Considering Risk Attitudes of Agents with VaR Constraints , 2011, IEEM 2011.

[4]  Samar K. Mukhopadhyay,et al.  A Stackelberg model of pricing of complementary goods under information asymmetry , 2011 .

[5]  H. Brian Hwarng,et al.  Understanding supply chain dynamics: A chaos perspective , 2008, Eur. J. Oper. Res..

[6]  X. Vives Duopoly information equilibrium: Cournot and bertrand , 1984 .

[7]  N. A. Huttly Book reviewModelling and optimization of complex systems: Proceedings of the IFIP-TC 7 working conference, Novosibirsk, USSR, 1978: G.I. Marchuk (Ed.) Volume 18 in: Lecture Notes in Control and Information Sciences, Springer, Berlin, 1979, vi + 293 pages, DM 28.50 , 1981 .

[8]  Louis Anthony Cox,et al.  Wiley encyclopedia of operations research and management science , 2011 .

[9]  E. Gal‐Or,et al.  Information Sharing in Oligopoly , 1985 .

[10]  J. Raju,et al.  Market Information and Firm Performance , 2000 .

[11]  Rajiv D. Banker,et al.  Quality and Competition , 1998 .

[12]  Yongjian Li,et al.  Pricing decisions for complementary products with firms' different market powers , 2013, Eur. J. Oper. Res..

[13]  Tönu Puu,et al.  The chaotic duopolists revisited , 1998 .

[14]  Junhai Ma,et al.  The Study of the Chaotic Behavior in Retailer's Demand Model , 2008 .

[15]  Youhua Chen,et al.  Customer and retailer rebates under risk aversion , 2011 .

[16]  Junhai Ma,et al.  The research on price game model and its complex characteristics of triopoly in different decision-making rule , 2013 .

[17]  Junhai Ma,et al.  Complexity analysis research of financial and economic system under the condition of three parameters’ change circumstances , 2012 .