Vertical Nash Game Research Articles

Delivery arrangement in online distribution channels under different power structures

Logistics delivery is a critical but costly operation in e-commerce. The e-retailer who sells products online may ask the supplier to ship products to customers, and the supplier responds by accepting or rejecting such a delivery proposal. Motivated by these observations, we consider an online distribution channel with two competing suppliers and one common e-retailer and analytically characterize the equilibrium delivery arrangement based on the nonlinear delivery cost in the E-retailer-Stackelberg, Supplier-Stackelberg, and Vertical-Nash games. Our analysis reveals that the market follower might be more willing to deliver products than the market leader in each Stackelberg game. Counterintuitively, the e-retailer prefers undertaking the delivery when there is a large delivery diseconomy under each power structure but prefers asking both suppliers to deliver products when there is a delivery economy (a small delivery diseconomy) in the E-retailer-Stackelberg and Vertical-Nash games (Supplier-Stackelberg game). The suppliers agree to ship products only when the delivery economy is apparent in the E-retailer-Stackelberg game but reject to do so in the Vertical-Nash game; in the Supplier-Stackelberg game, they accept the delivery proposal even though there is a significant delivery diseconomy. Although both suppliers can benefit from refusing to undertake the delivery when there is fierce competition in each Stackelberg game, interestingly, they still agree to do so and trap themselves in a prisoner's dilemma. In each Stackelberg game, only shifting the delivery responsibility to the suppliers might achieve a triple-win situation for the channel members, consumers, and society; in the Vertical-Nash game, however, this situation never occurs, and the consumer surplus and social welfare are invariant to the delivery arrangement.

Game Analysis of Dual-channel Supply Chain Based on Different Rights Structure

Based on members' different bargaining power in a dual channels system, this paper discusses the impact ofthree games on channel pricing, demand and members' profits by building Manufacturer Stackelberg, Retailer Stackelberg and Vertical Nash game model.The study finds that:(1) When the coefficient of cross-price elasticity of demand is 0, the effects of the three game strategies on the competitive equilibrium solution of the two-channel supply chain are undifferentiated. (2) When the coefficient of cross-price elasticity of demand is not 0, under the Stackelberg game dominated by the retailer (manufacturer), the traditional channel (direct channel) has the highest pricing, and the demand of the traditional channel (direct channel) is the smallest, while the demand of the traditional channel (demand of the direct channel) is the largest in the Stackelberg game dominated by the manufacturer (retailer); both manufacturers and retailers are willing to choose to give up their power and do the Stackelberg game. Both manufacturers and retailers are willing to give up power in favor of being a follower of the Stackelberg game, and the Nash game is always a strict downside for the game participants. Finally, the validity of the conclusions is further tested by case studies.

Investment strategy for renewable energy and electricity service quality under different power structures

<p style='text-indent:20px;'>This paper investigates and develops an electricity supply chain with an electricity generator and electricity retailer. The electricity generator invests in renewable energy and sells the electricity to the electricity retailer; the retailer then sells the electricity to consumers according to electricity service quality. Three models are considered: the vertical Nash game, the electricity-generator Stackelberg model, and the electricity-retailer Stackelberg model. Finally, the optimal solutions under different power-structure models are compared. Certain conclusions can be drawn from the findings: (1) the highest electricity service quality and renewable energy investment are obtained in the vertical Nash game model, the electricity generator obtains more profits in the electricity-generator Stackelberg model, and the electricity retailer obtains more profits in the electricity-retailer Stackelberg model. (2) The investment in renewable energy in the electricity-generator Stackelberg model is less than that in the electricity-retailer Stackelberg model, and the investment in electricity service quality in the electricity-retailer Stackelberg model is less than that in the electricity-generator Stackelberg model (under certain conditions). (3) Both increasing the electricity service quality sensitivity and renewable energy sensitivity could increase the optimal electricity price, electricity demand, electricity service quality, renewable energy investment, and supply-chain enterprises' profit.</p>

Operation strategy for new energy vehicle enterprises based on dual credit policy

<p style='text-indent:20px;'>This article constructs a two-stage supply chain consisting of a manufacturer (producing both fuel vehicles (FV) and new energy vehicles) and a retailer (selling both fuel vehicles and new energy vehicles) based on dual credit policy, considers three different power structure models, including the vertical Nash game model, the manufacturer Stackelberg game model, the retailer Stackelberg game model, and explores the operational strategy issues of new energy vehicle (NEV) enterprises under the dual credit policy. By comparing the optimal equilibrium solutions under different channel power structures, our findings indicate that (1) When the demand function is linear, the vertical Nash game model can achieve the highest system profit of the automotive supply chain, and in the manufacturer Stackelberg game model, the profit of the automaker is higher than that of the retailer, while in the retailer Stackelberg game model, the profit of the automaker is lower than that of the retailer. (2) The demand and pricing for FV and NEV in different models are determined by the range of FV and NEV production costs, credit trading prices, and the proportion of NEV credits. (3) Both the increase in the credit trading prices and the proportion of NEV credits will promote increased profits for the manufacturer and retailer. (4) The increase of the price sensitivity coefficient will reduce the demand as well as the profit of auto supply chain members.</p>

Research on Pricing Decision of Direct Sales Green Supply Chain Based on Consumers’ Valuation

Consumer’s valuation of merchandise is an important factor affecting consumer buying behavior. When the consumer’s valuation exceeds the price of product, the consumer generally makes a decision to purchase the product; conversely, when the consumer’s estimate is lower than the price of product, the consumer will usually refuse to buy the product. From the perspective of consumer product valuation, this study assumed that the consumer’s product valuation obeys a uniform distribution, and a novel consumer demand function was proposed. On this basis, we studied enterprises’ pricing decisions in the supply chain of green agricultural products and obtained the equilibrium prices and optimal profits of the enterprises in several different scenarios, including Vertical Nash game model (VNM), firm A Stackelberg game model (FASM), firm B Stackelberg game model (FBSM), and cooperative game model (CM). In addition, the influence of parameters, such as green level, green preference payment coefficient, and green cost on the optimal profit, was discussed based on game theory and numerical simulation analysis. It was found that equilibrium prices always existed in several different scenarios, and when consumer’s green preference payment coefficient was large enough, the optimal profit of firm B was greater than the optimal profit of firm A. Furthermore, in CM, the sum of optimal profit of firm A and optimal profit of firm B is maximum for four scenarios. Finally, in the three competitive scenarios, green level, green preference payment coefficient, and green cost, have a positive or negative effect on the optimal profits of firm A or firm B. The research conclusions of this study provided theoretical support for the decision-making of enterprises and related management departments.

Two‐period supply chain coordination strategies with ambidextrous sustainable innovations

AbstractThis study considers a manufacturer with ambidextrous sustainable innovation capability selling products in environmentally conscious market through an independent retailer in a two‐period game setting. We design a two‐period game theoretic and dyadic supply chain (SC) model considering exploitative and exploratory nature of environmental innovations. We study five different contract types, namely, wholesale price contract, vertical Nash game structure, cost sharing contract, revenue sharing contract and two‐part tariff contract. We demonstrate the impact of market sensitivity towards sustainable innovation and cost parameters on optimal level of decision parameters. The equilibrium results reveal that a suitably designed two‐part tariff contract can be used to achieve coordination in a fragmented SC. The equilibrium results assist managers to optimise the SC based on the two‐period contract model. The results obtained in this study can help the decision‐makers to take decisions on investment in the ambidextrous sustainable innovation under different types of contract structures.

Research on Quality Investment and Pricing Decision Sequence of Complex Equipment Supply Chain Considering Manufacturer's Incentive Strategy

For the demand uncertainty of complex equipment two-stage supply chain, the influence of different quality investment and pricing decision sequence on expected revenue and demand, with the consideration of incentive strategy between manufacturers to suppliers, manufacturer determines the basic quality and compensation for suppliers, suppliers determine the parts wholesale price and quality investment, then manufacturer decides the complex equipment product price. This paper set up two quality investment and price decentralized decision sequence: a Stackelberg game model, a vertical Nash game. Conditions of suppliers decisions are obtained, and the changes of pricing, quality investment, demand and profit of supply chain members are analyzed. It shows that making quality investment and wholesale price decisions simultaneously is best for manufacturers and integrated supply chain; determining quality investment and then set the wholesale price at the same time is the best choice for the whole suppliers. For individual suppliers, there is no absolutely dominant decision-making sequence. By comparing the model and different parameters, the paper provides a management basis for improving the quality and performance of supply chain subjects.

Study of game models and the complex dynamics of a low-carbon supply chain with an altruistic retailer under consumers’ low-carbon preference

This paper incorporates the retailer’s altruistic behavior into the low-carbon supply chain considering consumers’ low-carbon preference and establishes the Stackelberg game model and the vertical Nash game model from the perspectives of a static game and a dynamic game, respectively. First, the static analytical solutions of two models are obtained. Second, we explore the impacts of the retailer’s preference for altruism, consumers’ low-carbon preference and decision parameters on the complex nonlinear dynamic behaviors of the two models. The results show that the retailer’s altruistic behavior and consumers’ low-carbon preference narrow the stability region of the system. In the two game models, the retailer’s altruistic behavior always benefits the manufacture, but it is not good for the retailer; it is either beneficial to or not conducive for the whole supply chain. It is easier to make the system lose stability by accelerating the price adjustment parameter than by adjusting the carbon emission rate parameter. The higher adjustment parameter is even worse for the leader (the manufacturer) in the Stackelberg game, while in the vertical Nash game it is worse for the retailer. In addition, in the dynamic Stackelberg game, we are very surprised to find that a moderate consumer low-carbon preference is beneficial, but an excessive consumer low-carbon preference is not conducive to decision makers.

Game-Theoretic Analysis of Pricing Models in a Dyadic Supply Chain With Fairness Concerns

The existing studies on fairness in channel coordination assume markets as the group of oligopolies in which a few firms dominate, scant evidence has been provided where fairness concerns are investigated for a market scenario where all firms share equal dominance. This article considers a dyadic supply chain composed of one fair-minded manufacturer and one fair-minded retailer and investigate their pricing decisions under two different non-cooperative game-theoretic frameworks: manufacturer-led Stackelberg game and Vertical Nash game and provide a comparative analysis. The results show that the prices of the Stackelberg game model are always higher than that of the corresponding prices of the Vertical Nash game. We also find that the prices gap between the two models decreases with the retailer's fairness concern, and is uncertain with respect to manufacturer's fairness. In addition, the manufacturer's (retailer's) profit in the Stackelberg game is decreasing (increasing) in its own fairness and is uncertain in the Vertical Nash game. Furthermore, findings are illustrated through a numerical example.

Pricing and Carbon Emission Strategy of Supply Chain with Cap and Trade

Low-carbon economy is the trend of economic development in the future. It is gradually becoming a hot topic in academic and business circles that how to reduce carbon emissions. Cap and trade is one of the effective ways to reduce carbon emissions and has been adopted by many countries. We investigate a two-echelon supply chain that consists of a supplier and a manufacturer. This paper assumes a vertical Nash game between the two sides. We study three different models on cap and trade policy, which are the independent carbon reduction model and the concentrated models (only the supplier faces cap and trade and only the manufacturer faces cap and trade). We obtain the optimal decisions and unit carbon emissions of the supplier and the manufacturer. The optimal wholesale price, sale price, unit carbon emission and maximum profit under different cap and trade models have be compared by numerical analysis. We find that concentrated carbon reduction models are beneficial for supply chain enterprises, but as the price is creating more carbon emissions than the independent model. This study provides valuable managerial implications, which will be beneficial for firms to make an important strategy.

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

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.

Research on the complex features about a dual-channel supply chain with a fair caring retailer

This paper considers two different pricing policies in a dual-channel supply chain with a fair caring retailer. We establish two models: a Stackelberg game model in which the manufacturer acts as the leader and the retailer acts as the follower. The other one is a vertical Nash game model where the two firms have equal bargaining power and thus make decisions simultaneously. The models have demonstrated those dynamic behaviors, such as the bifurcation, periodic cycles and strange attractors of the systems. The influences of the fair concern coefficient and decision parameters on the complex nonlinear dynamics behaviors of the two models are analyzed through numerical simulation. The results show that in Stackelberg game model, the higher adjustment speed of the wholesale or the directly price is disadvantageous to manufacturer, but it is beneficial to retailer. In addition, in two game models, the excessive fairness concern is not always benefit to the retailer, it can also reduce the retailer’s profit. With the increase in the retailer’s fair concern coefficient, the total profits in two models both decrease while the total profits gap between two models gets better.

Product Line Pricing in a Supply Chain

A vertically integrated channel would prefer to coordinate the pricing of its products. In this paper, we investigate drivers of product line pricing decisions in a bilateral monopoly where a manufacturer produces and sells two substitutable or complementary products to a retailer. In a two-stage game, each firm commits credibly in the first stage to a pricing scheme within its own organization: product line pricing (PLP) or nonproduct line pricing (NPLP). In the second stage, depending on the relative balance of power in the supply chain, the firms engage in either a Nash or a leader-follower pricing game. We study the equilibrium of the two-stage game under a general symmetric demand function. With strategic interaction between firms, a firm may choose NPLP as the equilibrium pricing strategy. In particular, when the second stage is a leader-follower game, the price leader chooses PLP, and the follower may choose NPLP only if the inefficiency of using NPLP empowers the follower by increasing the demand sensitivity to the leader's margin. When the second stage is a vertical Nash game, whether NPLP occurs in equilibrium depends on the nature of coupling between demand interdependence and vertical strategic dependence: NPLP can be an equilibrium only if products are demand substitutes (complements) and vertical strategic dependencies are complementary (substitutable). We find that prisoner's dilemma exists in the first stage for both types of second-stage pricing games. In those cases, one firm may have the incentive to commit to a pricing scheme in the first stage prior to its channel partner and steer the supply chain away from prisoner's dilemma.

Intra-Firm Coordination of Product Management in a Supply Chain

A vertically integrated channel would prefer to coordinate the pricing of its products. In this paper, we investigate drivers of product line pricing decisions in a bilateral monopoly where a manufacturer produces and sells two substitutable or complementary products to a retailer. In a two-stage game, each firm commits credibly in the first stage to a pricing scheme within its own organization: product line pricing (PLP) or nonproduct line pricing (NPLP). In the second stage, depending on the relative balance of power in the supply chain, the firms engage in either a Nash or a leader-follower pricing game. We study the equilibrium of the two-stage game under a general symmetric demand function. With strategic interaction between firms, a firm may choose NPLP as the equilibrium pricing strategy. In particular, when the second stage is a leader-follower game, the price leader chooses PLP, and the follower may choose NPLP only if the inefficiency of using NPLP empowers the follower by increasing the demand sensitivity to the leader's margin. When the second stage is a vertical Nash game, whether NPLP occurs in equilibrium depends on the nature of coupling between demand interdependence and vertical strategic dependence: NPLP can be an equilibrium only if products are demand substitutes (complements) and vertical strategic dependencies are complementary (substitutable). We find that prisoner's dilemma exists in the first stage for both types of second-stage pricing games. In those cases, one firm may have the incentive to commit to a pricing scheme in the first stage prior to its channel partner and steer the supply chain away from prisoner's dilemma.

Empirical Analysis of Competitive Pricing Strategies with Complementary Product Lines

We build an econometric model of a household's purchase incidence and brand choice decisions in complementary product categories to account for cross-category dependence in demand. Complementarity is modeled as the additional utility that a household derives from the joint consumption of brands in complementary categories. We estimate the proposed multi-category demand model using scanner panel data on cake mix and frosting categories. Using the estimated demand model as an input, we investigate whether the observed retail prices in the two categories are consistent with joint-category profit maximization behavior on the part of the retailer. We also investigate whether manufacturers' pricing behavior is consistent with maximizing the sum of profits from their brands (bearing the same umbrella name) in both complementary categories. Lastly, we investigate the nature of vertical channel interactions between the manufacturers and the retailer. We find that our proposed multi-category demand model fits households' purchasing outcomes better than traditional single-category demand models (which yield significantly under-stated within-category price elasticities). While each brand in one category is a complement for every brand in the other category, the cross-category complementarity and cross-category price elasticity are found to be strongest with respect to the umbrella brand name in the other category. We find that the data are consistent with joint-category profit maximization behavior by the retailer across the two categories, and with a Vertical Nash game between the retailer and the manufacturer. Finally, we find that the data are consistent with a Bertrand-Nash pricing game among manufacturers maximizing the sum of their brands' profits in the two categories. In fact, joint-category profit maximization is found to be a dominant strategy for each manufacturer.