Stable Marketing Cooperation in a Differential Game for an Oligopoly

2018 ◽  
Vol 20 (03) ◽  
pp. 1750028 ◽  
Author(s):  
Mario A. García-Meza ◽  
Ekaterina Viktorovna Gromova ◽  
José Daniel López-Barrientos
Keyword(s):  
Finite Number ◽  
Dynamic Model ◽  
Differential Game ◽  
Cooperative Solution ◽  
Terminal Time ◽  
Marketing Cooperation ◽  
Number Of Firms

In this paper, we develop a dynamic model of an oligopoly playing an advertising game of goodwill accumulation with random terminal time. The goal is to find a cooperative solution that is time-consistent, considering a dynamic accumulation of goodwill with depreciation for a finite number of firms.

scholarly journals A Purusit Differential Game Problem on a Closed Convex Subset of a Hilbert Space

2020 ◽  
pp. 115-119
Author(s):  
Abbas Ja'afaru Badakaya ◽  
Bilyaminu Muhammad
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Finite Number ◽  
Differential Game ◽  
Convex Subset ◽  
Game Problem ◽  
Nonempty Closed Convex Subset ◽  
First Order ◽  
Control Functions ◽  
And Control

We study a pursuit differential game problem with finite number of pursuers and one evader on a nonempty closed convex subset of the Hilbert space l2. Players move according to certain first order ordinary differential equations and control functions of the pursuers and evader are subject to integral constraints. Pursuers win the game if the geometric positions of a pursuer and the evader coincide. We formulated and prove theorems that are concern with conditions that ensure win for the pursuers. Consequently, wining strategies of the pursuers are constructed. Furthermore, illustrative example is given to demonstrate the result.

Stable Marketing Cooperation in a Differential Game for an Oligopoly

2019 ◽  
pp. 377-394
Author(s):  
Mario A. García-Meza ◽  
Ekaterina Viktorovna Gromova ◽  
José Daniel López-Barrientos
Keyword(s):  
Differential Game ◽  
Marketing Cooperation

A DIFFERENTIAL GAME OF POLLUTION CONTROL WITH OVERLAPPING GENERATIONS

2014 ◽  
Vol 16 (03) ◽  
pp. 1450005 ◽  
Author(s):  
STEFAN WRZACZEK ◽  
EKATERINA SHEVKOPLYAS ◽  
SERGEY KOSTYUNIN
Keyword(s):  
Differential Game ◽  
Age Structure ◽  
Pollution Control ◽  
Overlapping Generations ◽  
Optimal Strategies ◽  
Overlapping Generations Model ◽  
Cooperative Solution ◽  
Altruistic Motive

We formulate an overlapping generations model on optimal emissions with continuous age structure. We compare the noncooperative solution to the cooperative one and obtain fundamental differences in the optimal strategies. Also including an altruistic motive does not avoid the problem of the myopic noncooperative solution. Finally we define a time-consistent tax scheme to obtain the cooperative solution in the noncooperative case.

scholarly journals Coordinating Carbon Emissions via Production Quantities: A Differential Game Approach

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Gila E. Fruchter ◽  
Hussein Naseraldin
Keyword(s):  
Nash Equilibrium ◽  
Environmental Pollution ◽  
Dynamic Model ◽  
Differential Game ◽  
Carbon Emissions ◽  
Industrial Sector ◽  
Total Output ◽  
Industrial Park ◽  
Social Planning ◽  
Feedback Strategies

Production emissions in the industrial sector are a major source of environmental pollution. In this paper, we explore how emission considerations are integrated with production decisions. We develop a dynamic model consisting of two firms located in the same industrial park, which satisfies exogenously given demands in separate markets. The two firms can build up or rundown stocks (full backlogging), both of which are costly. The emission cost depends on the total output of the two firms. We develop Nash equilibrium feedback strategies, where each firm decides on its output based on its inventory or the inventories of both. We also develop a social planning solution where decisions are centralized. We present the analytic results for the total profits in these settings. The results show the benefits of a decentralized approach over a centralized one, provided there is a mechanism for coordination. Finally, emission costs are compared for the various solution concepts.

scholarly journals Limit policies in N-sector dynamic growth games with externalities

1997 ◽  
Vol 1 (2) ◽  
pp. 81-87
Author(s):  
Ronald D. Fischer ◽  
Leonard J. Mirman
Keyword(s):  
Differential Game ◽  
Optimal Policy ◽  
Cooperative Solution ◽  
Dynamic Growth ◽  
Games With Externalities

We examine an economy with n production sectors that interact via a production externality. We find a solution to the resulting dynamic differential game between sectors and compare it to the cooperative solution. As the number of sectors increases, the limiting policy is the optimal policy without a production externality. This policy is inefficient and, depending on the sign of the externality between sectors, the inefficiency is due to over- (or under-) consumption.

scholarly journals Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1830
Author(s):  
Ekaterina Gromova ◽  
Anastasiia Zaremba ◽  
Shimai Su
Keyword(s):  
Differential Game ◽  
Cumulative Distribution Function ◽  
Time Consistency ◽  
Analytical Form ◽  
Payoff Function ◽  
Time Inconsistency ◽  
Cumulative Distribution ◽  
Cooperative Solution ◽  
Problem Of Time ◽  
Imputation Distribution Procedure

This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

scholarly journals Stochastic model of network formation with asymmetric players

2020 ◽  
Vol 12 (4) ◽  
pp. 62-92
Author(s):  
Пин Сунь ◽  
Ping Sun ◽  
Елена Михайловна Парилина ◽  
Elena Parilina
Keyword(s):  
Stochastic Model ◽  
Network Structure ◽  
Stochastic Games ◽  
Network Formation ◽  
Dynamic Consistency ◽  
Cooperative Solution ◽  
Joint Project ◽  
Cooperative Approach ◽  
Terminal Time ◽  
Theoretical Results

We propose a model of a network formation using the theory of stochastic games with random terminal time. Initially, the leader proposes a joint project in the form of a network to the players. Then, the players have the opportunities to form new links with each other to update the network proposed by the leader. Any player's payoff at any stage is determined by the network structure. It is also assumed that the formation of links proposed by the players is random. The duration of the game is also random. As a result of the players' actions and the implementation of the random steps of the Nature, a network is formed. We consider a cooperative approach to network formation, and we use the CIS-value as a cooperative solution. In this paper, a recurrent formula for its derivation in any cooperative subgame is obtained. The paper also investigates the dynamic consistency of CIS-value. The theoretical results are demonstrated by a numerical example.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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