Impact of price adjustment speed on the stability of Bertrand–Nash equilibrium and profit of the retailers

Kybernetes ◽  
2018 ◽  
Vol 47 (8) ◽  
pp. 1494-1523
Author(s):  
Rofin T.M. ◽  
Biswajit Mahanty
Keyword(s):  
Supply Chain ◽  
Nash Equilibrium ◽  
Chaotic Dynamics ◽  
Price Adjustment ◽  
Online Retailer ◽  
Content Type ◽  
Dual Channel ◽  
Adjustment Speed ◽  
The Stability ◽  
Dual Channel Supply Chain

Purpose The purpose of this paper is to investigate the impact of price adjustment speed on the stability of Bertrand–Nash equilibrium in the context of a dual-channel supply chain competition. Design/methodology/approach The paper considers a dual-channel supply chain comprising a manufacturer, a traditional retailer and an online retailer. A two-dimensional discrete dynamical system is used to examine the Bertrand competition between the retailers. The retailers are assumed to follow bounded rational expectations. Local stability of Bertrand–Nash equilibrium is investigated with respect to the price adjustment speed. Findings As the price adjustment speed increases, the stability of Bertrand–Nash equilibrium is lost, leading to complex chaotic dynamics. The results showed that chaotic dynamics deteriorates the profit of the retailers. The authors also found that the chaos can be controlled using an adaptive adjustment mechanism and the retailers enjoy higher profit when the chaos is controlled. Practical implications This study helps retail managers to choose an appropriate price adjustment speed to maximize profit. Originality/value The heterogeneity of the retailers is not considered in the studies involving dynamics of retailer competition. This paper contributes to the literature by considering the operational difference between a traditional retailer and an online retailer, i.e. price adjustment speed. In addition, the study establishes a link between price adjustment speed and profit.

Analysis of Pricing and Service Effort in Dual-Channel Supply Chains with Showrooming Effect

2020 ◽  
Vol 30 (16) ◽  
pp. 2050241
Author(s):  
Junhai Ma ◽  
Yaping Li ◽  
Zongxian Wang
Keyword(s):  
Supply Chain ◽  
Wholesale Price ◽  
Stable State ◽  
Dynamic Game ◽  
Price Adjustment ◽  
Flip Bifurcation ◽  
Stability Range ◽  
Dual Channel ◽  
Adjustment Speed ◽  
The Stability

Showrooming has become common practice of consumers in the context of dual-channel retailing. Under different intensities of showrooming, the manufacturer can decide whether to directly retail online (the M-R case) or resell through an e-retailer (the E-R case). Dual-channel supply chain models and dynamic game models are developed and both online selling formats are investigated. The dynamic game process of the supply chain is numerically simulated. The stability of the Nash equilibrium point is investigated by parameter basins for periodical cycles and bifurcation diagrams. The results show that the price adjustment speeds have a larger stability range in the M-R case while the service effort adjustment speed has a larger stability range in the E-R case. The stability of the systems is more sensitive to price adjustment speed than service effort adjustment speed in both supply chain structures. It is found that the systems will enter chaos through a flip bifurcation or a Neimark–Sacker bifurcation. The changes in attractors and basins of attraction indicate that both channels can reach the equilibria more easily when they choose a lower speed of retail price adjustment. The effects of showrooming on decision variables are greater in the M-R case than in the E-R case. When the showrooming effect is moderate, the manufacturer should choose the M-R case; when the showrooming effect is sufficiently large or sufficiently small, the manufacturer should choose the E-R case. We propose a wholesale price markdown strategy which can: (i) eliminate the double marginalization and coordinate the supply chain; (ii) effectively control the chaos caused by the overhigh adjustment speed of wholesale price, and restore the system to a stable state; (iii) improve the retailer’s service effort.

Dynamic pricing and coupon promotion strategies in a dual-channel supply chain based on differential game

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zonghuo Li ◽  
Wensheng Yang ◽  
Yinyuan Si
Keyword(s):  
Supply Chain ◽  
Differential Game ◽  
Dynamic Pricing ◽  
Brand Image ◽  
Content Type ◽  
Dual Channel ◽  
Promotion Policies ◽  
Promotion Strategies ◽  
Joint Pricing ◽  
Dual Channel Supply Chain

PurposeThis paper investigates a dual-channel supply chain in which a manufacturer offers coupons in the online channel and the retailer in the offline channel. The optimal pricing and coupon promotion policies are explored, and the brand image under different promotion scenarios is studied.Design/methodology/approachThree differential game models, namely no coupon is offered, coupons offered by the manufacturer and coupons offered by the retailer, are constructed.FindingsThe results show that the manufacturer and retailer intend to conduct coupon promotions under a large coupon redemption rate. Coupon promotion derives a higher price and profit for the issuers, and the manufacturer can free-ride on the retailer's coupon promotion. The retailer's profit in the retailer-promotion scenario may be lower than that in the manufacturer-promotion scenario in some special conditions. Besides, price, coupon face value, brand image and profit increase over time. After multiple cycles game, the operational strategy evolves to an optimal equilibrium status.Originality/valueThis paper provides guidance and advice for dual-channel supply enterprises to implement joint pricing and coupon promotion strategies under multiple sales seasons.

Study and Simulation on Dynamics of a Risk-Averse Supply Chain Pricing Model with Dual-Channel and Incomplete Information

2016 ◽  
Vol 26 (09) ◽  
pp. 1650146 ◽  
Author(s):  
Lijian Sun ◽  
Junhai Ma
Keyword(s):  
Supply Chain ◽  
Incomplete Information ◽  
Dynamic Pricing ◽  
Wholesale Price ◽  
Price Adjustment ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Risk Averse ◽  
Dual Channel ◽  
Adjustment Speed

Under the industrial background of dual-channel, volatility in demand of consumers, we use the theory of bifurcations and numerical simulation tools to investigate the dynamic pricing game in a dual-channel supply chain with risk-averse behavior and incomplete information. Due to volatility of demand of consumers, we consider all the players in the supply chain are risk-averse. We assume there exist Bertrand game and Manufacturers’ Stackelberg in the chain which are closer to reality. The main objective of the paper is to investigate the complex influence of the decision parameters such as wholesale price adjustment speed, risk preference and service value on stability of the risk-averse supply chain and average utilities of all the players. We lay emphasis on the influence of chaos on average utilities of all the players which did not appear in previous studies. The dynamic phenomena, such as the bifurcation, chaos and sensitivity to initial values are analyzed by 2D bifurcation phase portraits, Double Largest Lyapunov exponent, basins of attraction and so on. The study shows that the manufacturers should slow down their wholesale price adjustment speed to get more utilities, if the manufacturers are willing to take on more risk, they will get more profits, but they must keep their wholesale prices in a certain range in order to maintain the market stability.

The pricing strategy of dual-channel supply chain with risk-averse agents and heterogeneous preference consumers

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rufeng Wang ◽  
Zhiyong Chang ◽  
Shuli Yan
Keyword(s):  
Supply Chain ◽  
Risk Control ◽  
Optimal Strategies ◽  
Risk Attitude ◽  
Risk Attitudes ◽  
Risk Averse ◽  
Content Type ◽  
Dual Channel ◽  
Heterogeneous Preference ◽  
Dual Channel Supply Chain

PurposeThe purpose of this paper is to investigate the pricing strategy and the impact of agents' risk preference in a dual-channel supply chain in which both agents are risk-averse.Design/methodology/approachThe authors make use of the mean-variance (MV) method to measure the risk aversion of the agents and apply Stackelberg game to obtain the optimal strategies of the proposed models. Furthermore, the authors compare the optimal strategies with that in the benchmark model in which no agent is risk-averse.FindingsThe authors find that the pricing decisions can be divided into four categories according to the risk attitudes of the agents: the decisions that are independent of two agents' risk attitudes, the decisions that depend on only one agent’s risk attitude (i.e. depend on only manufacturer's risk attitude and depend on only retailer's risk attitude) and the decisions that depend on both agents' risk attitudes. In addition, the authors find that the retail price will be lower and the wholesale price in most cases will be lower than that in the benchmark when at least one agent's risk control is effective; the demand will be always increasing as long as one agent's risk control is effective. Furthermore, compared to the benchmark, a win-win strategy (i.e. Pareto improvement) for the supply chain members can be obtained in a certain range where the agents' risk controls are appropriate.Originality/valueThis research provides a theoretical reference for the managers to make the pricing decisions and the risk control in dual-channel supply chains with heterogeneous preference consumers.

Impact of wholesale price discrimination by the manufacturer on the profit of supply chain members

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rofin TM ◽  
Biswajit Mahanty
Keyword(s):  
Supply Chain ◽  
Price Discrimination ◽  
Wholesale Price ◽  
Price Strategy ◽  
Content Type ◽  
Dual Channel ◽  
Channel Preference ◽  
Online Channel ◽  
Dual Channel Supply Chain ◽  
The Impact

PurposeThe purpose of this paper is to investigate the impact of wholesale price discrimination by a manufacturer in a retailer–e-tailer dual-channel supply chain for different product categories based on their online channel preference.Design/methodology/approachThis paper considers a dual-channel supply chain comprising of a retailer and an e-tailer engaged in competition. Game-theoretic models are developed to model the competition between the retailer and e-tailer and to derive their optimal price, optimal order quantity and optimal profit under (1) equal wholesale price strategy and (2) discriminatory wholesale price strategy. Further, a numerical example was employed to quantify the results and to capture the variation with respect to online channel preference of the product.FindingsIt is beneficial for the manufacturer to adopt a discriminatory wholesale price strategy for products having both high online channel preference and low online channel preference. However, equal wholesale price strategy is beneficial for the e-tailer and the retailer in the case of products having high online channel preference and in the case of products having low online channel preference, respectively.Practical implicationsThe study helps the manufacturers to maximize their profit by adopting the right wholesale price strategy considering the online channel preference of the product when the manufacturers are supplying to heterogeneous retailers.Originality/valueThere is scant literature on the wholesale price strategy of the manufacturer considering the heterogeneous downstream retailers. This paper contributes the literature by bridging this gap. In addition, the study establishes a link between the wholesale price strategy and online channel preference of the product.

A collaborative scenario-based decision model for a disrupted dual-channel supply chain

2019 ◽  
Vol 27 (3) ◽  
pp. 933-957 ◽  
Author(s):  
Jafar Heydari ◽  
Amin Aslani ◽  
Ali Sabbaghnia
Keyword(s):  
Decision Making ◽  
Supply Chain ◽  
Distribution Systems ◽  
Channel Coordination ◽  
Content Type ◽  
Pricing Decisions ◽  
Collaboration Model ◽  
Dual Channel ◽  
Decentralized Decision Making ◽  
Dual Channel Supply Chain

Purpose Distribution systems usually utilize both traditional retailing channels in conjunction with e-channels. The purpose of this paper is to investigate a dual-channel supply chain, comprising a traditional retailing channel and an e-channel under disruption. By benchmarking against the centralized decision structure, the authors intend to propose a collaboration model to achieve channel coordination as well as more reliable decisions. Design/methodology/approach Four different channel disruption scenarios, with customers’ reaction toward disruptions, are examined, and then, optimal pricing decisions for both centralized and decentralized decision-making structures are extracted. Next, a collaboration mechanism based on the dominancy power of channel members is developed to entice all channel members to participate in channel coordination. By benchmarking the proposed collaboration model against both the decentralized/centralized structures a win–win solution is guaranteed for all channel members. In addition, the proposed model ensures more reliable decisions than the centralized structure, as it guarantees less fluctuated income levels. Findings This study shows, as the disruption probability grows, the channel profit decreases while the channel-retailing price increases. Furthermore, the exact alignment of the centralized decision-making approach and the proposed collaboration model is not achievable due to the problem infeasibility. Numerical experiments and sensitivity analyses benchmark the performance of the proposed collaboration mechanism against the centralized structure for the full alignment with centralized decision-making approach. Originality/value This study contributes to the channel conflict literature as jointly considers pricing decisions, disruptions and coordination. Further, consumers’ reaction toward disruption is analyzed through a transshipment agreement.

scholarly journals The Complexity Analysis in Dual-Channel Supply Chain Based on Fairness Concern and Different Business Objectives

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Li Qiu-xiang ◽  
Zhang Yu-hao ◽  
Huang Yi-min
Keyword(s):  
Supply Chain ◽  
Control Method ◽  
Complexity Analysis ◽  
Business Objectives ◽  
Dual Channel ◽  
The Stability ◽  
Fairness Concern ◽  
High Level ◽  
Dual Channel Supply Chain ◽  
Supply Chain Operation

We study a dual-channel supply chain which consists of one dual-channel manufacturer and one traditional retailer considering fairness concern. The manufacturer takes the market share as one of its business objectives in the competition game. We are devoted to establishing a vertical Nash game model and analyzing the price evolution of the model via the method of complexity theory and take adaptive adjustment control method to control the system’s chaotic state. The results show that an excessive price adjustment speed will hurt the system’s stability as well as profit of the supply chain. A high level fair caring for retailer will push the system to fall into chaos earlier, while a higher level fair caring for manufacturer will enlarge the stability region of the system. Setting the different objectives by the manufacturer will cause drastic competition in dual-channel supply chain. The research of this paper is of great significance to the decision-makers’ price decision and supply chain operation management.

scholarly journals The Entropy Complexity of an Asymmetric Dual-Channel Supply Chain with Probabilistic Selling

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 543 ◽  
Author(s):  
Yimin Huang ◽  
Qiuxiang Li
Keyword(s):  
Supply Chain ◽  
Stable State ◽  
Channel Structure ◽  
Flip Bifurcation ◽  
Supply Chain System ◽  
Chain System ◽  
Dual Channel ◽  
Decision Variables ◽  
The Stability ◽  
Dual Channel Supply Chain

Considering consumers’ attitudes to risks for probabilistic products and probabilistic selling, this paper develops a dynamic Stackelberg game model of the supply chain considering the asymmetric dual-channel structure. Based on entropy theory and dynamic theory, we analyze and simulate the influences of decision variables and parameters on the stability and entropy of asymmetric dual-channel supply chain systems using bifurcation, entropy diagram, the parameter plot basin, attractor, etc. The results show that decision variables and parameters have great impacts on the stability of asymmetric dual-channel supply chains; the supply chain system will enter chaos through flip bifurcation or Neimark–Sacker bifurcation with the increase of the system entropy, and thus the system is more complex and falls into a chaotic state, with its entropy increased. The stability of the system can become robust with the increase of the probability that product a becomes a probabilistic product, and it weakens with the increase of the risk preference of customers for probabilistic products and the relative bargaining power of the retailer. A manufacturer using the direct selling channel may obtain greater profit than one using traditional selling channels. Using the method of parameter adjustment and feedback control, the entropy of the supply chain system will decline, and the supply chain system will fall into a stable state. Therefore, in the actual market of probabilistic selling, the manufacturers and retailers should pay attention to the parameters and adjustment speed of prices and ensure the stability of the game process and the orderliness of the dual-channel supply chain.

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