A differential game model of Nash equilibrium on a congested traffic network

Networks ◽  
1993 ◽  
Vol 23 (6) ◽  
pp. 557-565 ◽  
Author(s):  
Byung-Wook Wie
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Game Model ◽  
Traffic Network ◽  
Congested Traffic

scholarly journals Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 132
Author(s):  
Valery Y. Glizer
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Cheap Control ◽  
Optimal Values ◽  
Definition Of ◽  
Zero Sum ◽  
Equilibrium Sequence

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

Manufacturing service order allocation in the context of social manufacturing based on Stackelberg game

2018 ◽  
Vol 233 (8) ◽  
pp. 1890-1901
Author(s):  
Wei Guo ◽  
Pingyu Jiang
Keyword(s):  
Quality Of Service ◽  
Nash Equilibrium ◽  
Manufacturing Industry ◽  
Stackelberg Game ◽  
Game Model ◽  
Service Cost ◽  
Order Allocation ◽  
Multi Objective ◽  
Bird Swarm Algorithm

For adapting the socialization, individuation and servitization in manufacturing industry, a new manufacturing paradigm called social manufacturing has received a lot of attention. Social manufacturing can be seen as a network that enterprises with socialized resources self-organized into communities that provide personalized machining and service capabilities to customers. Since a community of social manufacturing has multiple enterprises and emphasizes on the importance of service, manufacturing service order allocation must be studied from the new perspective considering objectives on service cost and quality of service. The manufacturing service order allocation can be seen as a one-to-many game model with multi-objective. In this article, a Stackelberg game model is proposed to tackle the manufacturing service order allocation problem with considering the payoffs on cost and quality of service. Since this Stackelberg game can be mapped to a multi-objective bi-level programming, a modified multi-objective hierarchical Bird Swarm Algorithm is used to find the Nash equilibrium of the game. Finally, a case from a professional printing firm is analyzed to validate the proposed methodology and model. The objective of this research is to find the Nash equilibrium on the manufacturing service order allocation and provide strategies guidance for customer and small- and medium-sized enterprises with optimal service cost and lead time. According to the game process and Nash equilibrium, some rules are revealed, and they are useful for guiding practical production.

scholarly journals Feedback Nash Equilibrium of N Agents Fishery Problem

2021 ◽  
Vol 14 (5) ◽  
pp. 78
Author(s):  
Letian Jiao ◽  
Haitao Chen
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Feedback Nash Equilibrium ◽  
Common Resource ◽  
Resource Stock

This paper is built on the fundamental of Jorgensen and Sorge considering a differential game about fishery problem. In reality, the exploiters can be many because of the non-excludability of common resource. Thus, we expand the former two players model to N players model and we find more different equilibriums in N players scenario. Through this, we want to find some guidance for the changing of common resource stock. Further to control overexploitation.

The three kinds of degree distributions and nash equilibrium on the limiting random network

2019 ◽  
Vol 20 (05) ◽  
pp. 2050033
Author(s):  
Dong Han ◽  
Min Xia
Keyword(s):  
Nash Equilibrium ◽  
Random Network ◽  
Sufficient Conditions ◽  
Curved Surface ◽  
High Dimensional ◽  
Game Model ◽  
Curved Surfaces

A generalized dynamically evolving random network and a game model taking place on the evolving network are presented. We show that there exists a high-dimensional critical curved surface of the parameters related the probabilities of adding or removing vertices or edges such that the evolving network may exhibit three kinds of degree distributions as the time goes to infinity when the parameters belong to the super-critical, critical and sub-critical curved surfaces, respectively. Some sufficient conditions are given for the existence of a regular Nash equilibrium which depends on the three kinds of degree distributions in the game model on the limiting random network.

An Analysis of Enterprise Investment Decision Based on Cournot-Nash Equilibrium

2010 ◽  
Vol 40-41 ◽  
pp. 497-505
Author(s):  
Hua Qi Chai ◽  
De Qiang Song ◽  
Shu Juan Luo
Keyword(s):  
Nash Equilibrium ◽  
Numerical Method ◽  
Investment Decision ◽  
Sunk Costs ◽  
Operating Costs ◽  
Game Model ◽  
Market Demand ◽  
Comparative Advantages ◽  
Enterprise Investment ◽  
Higher Sensitivity

Cournot-Nash equilibrium is introduced into the traditional options game model, and the manifestation of this model under the condition is studied. Besides, a numerical method is used for solving investment values and thresholds of the leader enterprise and the follower enterprise. The results showed that both enterprises still have determined investment thresholds under Cournot-Nash equilibrium. In contrast, the follower enterprise investment threshold has a higher sensitivity to its own factors, but its present investment value is less subject to its own threshold and market demand; the leader enterprise performs contrary to the follower. Comparative advantages of marginal operating costs and investment sunk costs determine enterprise roles.

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