The Complexity Analysis for Price Game Model of Risk-Averse Supply Chain Considering Fairness Concern

This paper, considering risk aversion and fair concern, establishes a dynamic price game model of a dual-channel supply chain in which dual-channel retailer sells products through traditional channel and online channel and the online retailer only sells products through online channel. The stability of the system and the influences of different parameter values on utilities are analyzed emphatically using game theory and nonlinear dynamic theory, such as 2D and 3D bifurcation diagram, parameter plot basin, chaos attractor, and sensitivity to initial value. The results find that the system is more likely to lose stability and fall into chaos with the customer demand fluctuating greatly. The system enters into chaos through flip bifurcation with the increase of the price adjustment speed; adjusting the risk-aversion levels or the fairness concern levels of the two retailers can make the system be in a stable state or delay the occurrence of system instability. When the system is in chaos, the average utility of the online retailer will decrease and one of the dual-channel retailers will increase. Using the state feedback control method, the system can return to a stable state from chaos by selecting appropriate control parameters. The research of this paper is of great significance to the decision-makers’ price decision and supply chain operation management.

[1]  K. J. Ray Liu,et al.  Indirect Reciprocity Security Game for Large-Scale Wireless Networks , 2012, IEEE Transactions on Information Forensics and Security.

[2]  Yi-Min Huang,et al.  The Entropy Complexity of an Asymmetric Dual-Channel Supply Chain with Probabilistic Selling , 2018, Entropy.

[3]  Bo Li,et al.  Dual-channel supply chain equilibrium problems regarding retail services and fairness concerns , 2016 .

[4]  E. Fehr.  A Theory of Fairness, Competition and Cooperation , 1998 .

[5]  Tony Haitao Cui,et al.  Fairness and Channel Coordination , 2007, Manag. Sci..

[6]  Junhai Ma,et al.  Complex Dynamics in a Triopoly Game with Multiple Delays in the Competition of Green Product Level , 2018, Int. J. Bifurc. Chaos.

[7]  Hêris Golpîra,et al.  Supply Chain Network Design Optimization with Risk-Averse Retailer , 2017, Int. J. Inf. Syst. Supply Chain Manag..

[8]  Liu Tian-zhuo.  Supply chain coordination considering fairness concerns , 2010 .

[9]  Zigang Zhang,et al.  Pricing Strategy in Risk-Averse Dual-channel Supply Chain , 2012 .

[10]  Junhai Ma,et al.  Implications of stochastic demand and manufacturers’ operational mode on retailer's mixed bundling strategy and its complexity analysis , 2018 .

[11]  Hongxiong Yang,et al.  A study on pricing decision of supply chain based on fairness concern , 2017 .

[12]  Elena Katok,et al.  Fairness and Coordination Failures in Supply Chain Contracts , 2011 .

[13]  M. R. Amin-Naseri,et al.  Price competition between two leader–follower supply chains with risk-averse retailers under demand uncertainty , 2015 .

[14]  C. T. Ng,et al.  Impact of risk aversion on optimal decisions in supply contracts , 2010 .

[15]  H. Vincent Poor,et al.  User-Centric View of Jamming Games in Cognitive Radio Networks , 2015, IEEE Transactions on Information Forensics and Security.

[16]  Junhai Ma,et al.  Complexity Analysis About Nonlinear Mixed Oligopolies Game Based on Production Cooperation , 2018, IEEE Transactions on Control Systems Technology.

[17]  T. Puu,et al.  On the Stability of Cournot Equilibrium when the Number of Competitors Increases , 2018 .

[18]  Bo Li,et al.  Cooperative advertising in a dual-channel supply chain with a fairness concern of the manufacturer , 2015 .

[19]  ChiangWei-yu Kevin,et al.  Direct Marketing, Indirect Profits: A Strategic Analysis of Dual-Channel Supply-Chain Design , 2003 .

[20]  Coordinating a two-level supply chain with risk-averse preferences based on revenue-sharing contract , 2008, 2008 27th Chinese Control Conference.

[21]  Hao Ren,et al.  Research on the Complexity and Chaos Control about a Closed-Loop Supply Chain with Dual-Channel Recycling and Uncertain Consumer Perception , 2018, Complex..

[22]  Texas Dallas.  Channel Coordination with a Risk-Neutral Supplier and a Downside-Risk-Averse Retailer , 2005 .

[23]  Fang Zhang,et al.  Research on the complex features about a dual-channel supply chain with a fair caring retailer , 2016, Commun. Nonlinear Sci. Numer. Simul..

[24]  Bo Li,et al.  Dual-channel supply chain pricing decisions with a risk-averse retailer , 2014 .

[25]  Jie Zhang,et al.  Impact of channel power and fairness concern on supplier’s market entry decision , 2017, J. Oper. Res. Soc..

[26]  Junhai Ma,et al.  The equilibrium, complexity analysis and control in epiphytic supply chain with product horizontal diversification , 2018 .