scholarly journals Infinity Period Dynamic Control of a Kind of Channel’s Price and Brand Investment: A Differential Game Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Kaihong Wang ◽  
Li Cheng ◽  
Chuan Ding
Keyword(s):  
Control Problem ◽  
Differential Game ◽  
Dynamic Optimization ◽  
Stackelberg Game ◽  
Dynamic Control ◽  
Distribution Channel ◽  
Optimization Theory ◽  
Retail Price ◽  
Hamilton Function ◽  
Static Game

The infinity period dynamic control problem of distribution channel was studied with differential game approach. Four differential dynamic control models of coordinated channel game, uncoordinated static game, Stackelberg game with manufacture controlled, and Stackelberg game withnretailers controlled were constructed. Some results applied dynamic optimization theory made with Hamilton function. The conclusions are as follows. (1) Optimization brand investment controlled by manufacture has nothing to do with time. (2) Retail price was the most minimum when channel was integrated. (3) Manufacture’s profits of uncoordinated static game and Stackelberg game with manufacture controlled were more than Stackelberg game withnretailers controlled. (4) Retailer’s profits of Stackelberg game withnretailers controlled were less than Stackelberg game with manufacture controlled. (5) Channel’s total profits of Stackelberg game withnretailers controlled were the most minimum.

scholarly journals Strategic Analysis of the Pricing Mechanisms in an Online Book Supply Chain in the Presence of Reference Price Effects

2021 ◽  
Vol 16 (5) ◽  
pp. 1492-1516
Author(s):  
Wenhua Hou ◽  
Yuwen Zeng
Keyword(s):  
Supply Chain ◽  
Discount Rate ◽  
Reference Price ◽  
Stackelberg Game ◽  
Lower Boundary ◽  
Retail Price ◽  
Reference Points ◽  
Price Effects ◽  
Retail Prices ◽  
Online Book

(1) Background: A binding recommended retail price has been used in several markets in a variety of forms, and the book market is a typical example. Publishers sell books to online retailers at a unit wholesale discount computed on the cover price. Retailers are then allowed to set the retail price. Therefore, if consumers regard the cover prices as reference points, then they may be more likely to purchase books if retail prices are lower than the cover prices. (2) Methods: We develop a Stackelberg game model for a book supply chain to investigates how reference price effects affect retailers and publisher’s pricing strategies. (3) Results: The results show that retailers will sell printed books at a discount only when the publisher’s wholesale discount rate is not high. Further, as the intensity of the reference price effects increases, (a) the lower boundary of the wholesale discount rate rises, (b) publishers’ profits increase and (c) retailers’ profits increase relative to the level of consumers’ e-books acceptance. (4) Conclusions: This result is related to the fact that the online retailer, such as Amazon and JD.com, like to invoke reference price effects in consumers’ minds by highlighting the printed book’s discount rate.

scholarly journals A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environment

2018 ◽  
Vol 16 (1) ◽  
pp. 607-622 ◽  
Author(s):  
Shi Yin ◽  
Baizhou Li
Keyword(s):  
Differential Game ◽  
Cooperative Game ◽  
Stackelberg Game ◽  
Innovation System ◽  
Stochastic Differential Game ◽  
Low Carbon ◽  
Nash Game ◽  
Low Carbon Economy ◽  
Collaborative Innovation ◽  
Technology Level

AbstractConsidering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.

The Mathematics of Coordinated Control of Prosthetic Arms and Manipulators

1972 ◽  
Vol 94 (4) ◽  
pp. 303-309 ◽  
Author(s):  
D. E. Whitney
Keyword(s):  
Control Problem ◽  
Rate Control ◽  
Position Control ◽  
Dynamic Control ◽  
Mathematical Formulation ◽  
Coordinated Control ◽  
Computer Assisted ◽  
Final Position ◽  
Coordinate Systems ◽  
Joint Angles

The problems of coordinated rate control and position control of multidegree-of-freedom arms are treated together in this paper. A mathematical formulation is presented which allows real time computer-assisted rate control under a variety of external coordinate systems. A new solution to the endpoint position control problem is given, allowing the arm to be driven to a final position specified in meaningful external coordinates without the corresponding final joint angles being known. Attention is given to redundant arms, to the possibility of singularities, and to the relation between this work and dynamic control of arms.

scholarly journals Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Hsun-Jung Cho ◽  
You-Heng Huang
Keyword(s):  
Control Problem ◽  
Network Flows ◽  
Stackelberg Game ◽  
Nonlinear Approximation ◽  
Second Order ◽  
Signal Control ◽  
Reaction Function ◽  
Lower Level Problem ◽  
Level Problem ◽  
Upper Level

The equilibrium network signal control problem is represented as a Stackelberg game. Due to the characteristics of a Stackelberg game, solving the upper-level problem and lower-level problem iteratively cannot be expected to converge to the solution. The reaction function of the lower-level problem is the key information to solve a Stackelberg game. Usually, the reaction function is approximated by the network sensitivity information. This paper firstly presents the general form of the second-order sensitivity formula for equilibrium network flows. The second-order sensitivity information can be applied to the second-order reaction function to solve the network signal control problem efficiently. Finally, this paper also demonstrates two numerical examples that show the computation of second-order sensitivity and the speed of convergence of the nonlinear approximation algorithm.

Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

2014 ◽  
Vol 1042 ◽  
pp. 172-177
Author(s):  
Guang Yan Xu ◽  
Ping Li ◽  
Biao Zhou
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Differential Game ◽  
Numerical Solutions ◽  
Game Problem ◽  
Gap Function ◽  
Differential Variational Inequality ◽  
Air Combat

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

A STACKELBERG GAME OF INNOVATION DIFFUSION: PRICING, ADVERTISING AND SUBSIDY STRATEGIES

2001 ◽  
Vol 03 (04) ◽  
pp. 325-339 ◽  
Author(s):  
LUIGI DE CESARE ◽  
ANDREA DI LIDDO
Keyword(s):  
Innovation Diffusion ◽  
Differential Game ◽  
Stackelberg Game ◽  
New Product ◽  
Public Authority ◽  
Optimal Price ◽  
Advertising Strategy ◽  
Stackelberg Differential Game ◽  
Set Up

We consider a firm that wishes to maximise the profits coming from the sale of a new product or technology by determining an optimal price and advertising strategy. A public authority wishes to accelerate and stimulate the adoption of the new product by using a budget to give price subsidies directly to the consumers. The problem is set up as a Stackelberg differential game.

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