Computing Pareto–Nash Equilibrium Sets in Finite Multi-Objective Mixed-Strategy Games

2018 ◽  
pp. 217-244
Author(s):  
Valeriu Ungureanu
Keyword(s):  
Nash Equilibrium ◽  
Mixed Strategy ◽  
Multi Objective ◽  
Strategy Games

scholarly journals Multi-objective Optimization of Accommodation Capacity for Distributed Generation Based on Mixed Strategy Nash Equilibrium, Considering Distribution Network Flexibility

2019 ◽  
Vol 9 (20) ◽  
pp. 4395 ◽  
Author(s):  
Weisheng Liu ◽  
Jian Wu ◽  
Fei Wang ◽  
Yixin Huang ◽  
Qiongdan Dai ◽  
...  
Keyword(s):  
Nash Equilibrium ◽  
Distributed Generation ◽  
Mixed Strategy ◽  
Distribution Network ◽  
Distribution Networks ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Mixed Strategy Nash Equilibrium ◽  
Network Flexibility ◽  
Strategy Nash Equilibrium

The increasing penetration of distributed generation (DG) brings about great fluctuation and uncertainty in distribution networks. In order to improve the ability of distribution networks to cope with disturbances caused by uncertainties and to evaluate the maximum accommodation capacity of DG, a multi-objective programming method for evaluation of the accommodation capacity of distribution networks for DG is proposed, considering the flexibility of distribution networks in this paper. Firstly, a multi-objective optimization model for determining the maximum accommodation of DG by considering the flexibility of distribution networks is constructed, aiming at maximizing the daily energy consumption, minimizing the voltage amplitude deviation, and maximizing the line capacity margin. Secondly, the comprehensive learning particle swarm optimization (CLPSO) algorithm is used to solve the multi-objective optimization model. Then, the mixed strategy Nash equilibrium is introduced to obtain the frontier solution with the optimal joint equilibrium value in the Pareto solution set. Finally, the effectiveness of the proposed method is demonstrated with an actual distribution network in China. The simulation results show that the proposed planning method can effectively find the Pareto optimal solution set by considering multiple objectives, and can obtain the optimal equilibrium solution for DG accommodation capacity and distribution network flexibility.

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.

THE MIXED STRATEGY NASH EQUILIBRIUM OF THE TELEVISON NEWS SCHEDULING GAME

2008 ◽  
Vol 56 (2) ◽  
pp. 418-418 ◽  
Author(s):  
JEAN J. GABSZEWICZ ◽  
DIDIER LAUSSEL ◽  
MICHEL LE BRETON
Keyword(s):  
Nash Equilibrium ◽  
Mixed Strategy ◽  
Mixed Strategy Nash Equilibrium ◽  
Strategy Nash Equilibrium
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