An Infinite Horizon Differential Game of Optimal CLV-Based Strategies with Non-atomic Firms

2016 ◽  
pp. 111-130
Author(s):  
Gerasimos Lianos ◽  
Igor Sloev
Keyword(s):  
Differential Game ◽  
Infinite Horizon

SHELF-SPACE ALLOCATION AND ADVERTISING DECISIONS IN THE MARKETING CHANNEL: A DIFFERENTIAL GAME APPROACH

2005 ◽  
Vol 07 (03) ◽  
pp. 313-330 ◽  
Author(s):  
GUIOMAR MARTÍN-HERRÁN ◽  
SIHEM TABOUBI
Keyword(s):  
Differential Game ◽  
Infinite Horizon ◽  
Marketing Channel ◽  
Marketing Channels ◽  
Value Functions ◽  
Shelf Space ◽  
Space Allocation ◽  
Stackelberg Differential Game ◽  
Feedback Equilibria ◽  
Shelf Space Allocation

This paper deals with the issue of shelf-space allocation and advertising decisions in marketing channels. We consider a network composed of a unique retailer offering the products of two competing manufacturers. The retailer controls the amount of shelf-space to allocate to both brands, while the manufacturers make advertising decisions in order to build their brand image (i.e. the goodwill stock). The demand for each brand is affected by its own goodwill level and the shelf-space allocated to the brand at retailer's store. The problem is formulated as a Stackelberg differential game played over an infinite horizon, with the manufacturers as leaders and the retailer as the follower. Stationary feedback equilibria are computed. Our main results indicate that the shelf-space allocated to each brand, manufacturers' advertising strategies at the equilibrium and channel members' value functions are affected by the goodwill levels of both products.

THE COMPETITION BETWEEN INTERNET SERVICE QUALITIES FROM A DIFFERENCE GAME VIEWPOINT

2012 ◽  
Vol 14 (01) ◽  
pp. 1250001 ◽  
Author(s):  
JOEL BLOT ◽  
NAILA HAYEK ◽  
FERHAN PEKERGIN ◽  
NIHAL PEKERGIN
Keyword(s):  
Differential Game ◽  
Optimal Control Problems ◽  
Service Providers ◽  
Infinite Horizon ◽  
Quality Of Services ◽  
Control Problems ◽  
Dynamical Modeling ◽  
Internet Service ◽  
Time Differential

We treat the competition between two Internet Service Providers which are distinguished by the Quality of Services that they propose. We model this competition by means of an infinite-horizon discrete-time differential game. The dynamical modeling is due to the presence of investments of the firms. We solve the problem by using several Pontryagin principles for the optimal control problems associated to this differential game. We obtain the existence and the uniqueness of a Markov–Nash equilibrium of this differential game.

scholarly journals Stochastic Differential Game-Based Malware Propagation in Edge Computing-Based IoT

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Li Miao ◽  
Shuai Li
Keyword(s):  
Differential Game ◽  
Infinite Horizon ◽  
Optimal Strategies ◽  
Edge Computing ◽  
Game Model ◽  
Stochastic Differential Game ◽  
Equilibrium Solutions ◽  
Stochastic Fluctuations ◽  
Malware Propagation ◽  
Nash Equilibrium Solutions

Internet of Things (IoT) has played an important role in our daily life since its emergence. The applications of IoT cover from the traditional devices to intelligent equipment. With the great potential of IoT, there comes various kinds of security problems. In this paper, we study the malware propagation under the dynamic interaction between the attackers and defenders in edge computing-based IoT and propose an infinite-horizon stochastic differential game model to discuss the optimal strategies for the attackers and defenders. Considering the effect of stochastic fluctuations in the edge network on the malware propagation, we construct the Itô stochastic differential equations to describe the propagation of the malware in edge computing-based IoT. Subsequently, we analyze the feedback Nash equilibrium solutions for our proposed game model, which can be considered as the optimal strategies for the defenders and attackers. Finally, numerical simulations show the effectiveness of our proposed game model.

scholarly journals A Cooperative Stochastic Differential Game of Transboundary Industrial Pollution between Two Asymmetric Nations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yongxi Yi ◽  
Rongwei Xu ◽  
Sheng Zhang
Keyword(s):  
Differential Game ◽  
Pollution Control ◽  
Industrial Pollution ◽  
Stackelberg Game ◽  
Infinite Horizon ◽  
Pollution Abatement ◽  
Transboundary Pollution ◽  
Stochastic Differential Game ◽  
Tax Rate ◽  
Consistent Solution

Considering the fact that transboundary pollution control calls for the cooperation between interested parties, this paper studies a cooperative stochastic differential game of transboundary industrial pollution between two asymmetric nations in infinite-horizon level. In this paper, we model two ways of transboundary pollution: one is an accumulative global pollutant with an uncertain evolutionary dynamic and the other is a regional nonaccumulative pollutant. In our model, firms and governments are separated entities and they play a Stackelberg game, while the governments of the two nations can cooperate in pollution reduction. We discuss the feedback Nash equilibrium strategies of governments and industrial firms, and it is found that the governments being cooperative in transboundary pollution control will set a higher pollution tax rate and make more pollution abatement effort than when they are noncooperative. Additionally, a payment distribution mechanism that supports the subgame consistent solution is proposed.

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