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Nash Equilibrium In Game Theory ~xRay Pixy

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 Video Link  CLICK HERE... Learn Nash Equilibrium In Game Theory Step-By-Step Using Examples. Video Chapters: Nash Equilibrium  00:00 Introduction 00:19 Topics Covered 00:33 Nash Equilibrium  01:55 Example 1  02:30 Example 2 04:46 Game Core Elements 06:41 Types of Game Strategies 06:55  Prisoner’s Dilemma  07:17  Prisoner’s Dilemma Example 3 09:16 Dominated Strategy  10:56 Applications 11:34 Conclusion The Nash Equilibrium is a concept in game theory that describes a situation where no player can benefit by changing their strategy while the other players keep their strategies unchanged.  No player can increase their payoff by changing their choice alone while others keep theirs the same. Example : If Chrysler, Ford, and GM each choose their production levels so that no company can make more money by changing their choice, it’s a Nash Equilibrium Prisoner’s Dilemma : Two criminals are arrested and interrogated separately. Each has two ...

PSO Python Code || Particle Swarm Optimization in Python || ~xRay Pixy


Particle Swarm Optimization Implementation in Python Video Chapters: 00:00 Introduction 02:01 Code 05:55 Position Initialization 08:06 PSO Main Loop 08:42 Velocity Calculation 10:02 Position Update 10:36 Fitness Evaluation 13:21 Objective Function 17:44 Result 19:00 Conclusion

.....................................................SOURCE CODE.........................................................................
import random import numpy as np from tkinter import messagebox #Define Class Particles class Particle: def __init__ (self,position): self.position=position self.velocity=np.zeros_like(position) self.best_position=position self.best_fitness=float('inf') def PSO(ObjF,Pop_Size,D,MaxT): swarm_best_position=None swarm_best_fitness=float('inf') particles=[] #Posotion Initialization position=np.random.uniform(-0.5,0.5,D) particle=Particle(position) particles.append(particle) #Fitness Update fitness=ObjF(position) if fitness<swarm_best_fitness: swarm_best_fitness=fitness swarm_best_position=position particle.best_position=position particle.best_fitness=fitness #PSO Main Loop for itr in range(MaxT): for particle in particles: #Update Velocity w = 0.8 c1 = 1.2 c2 = 1.2 r1=random.random() r2=random.random() #Velocity Calculation particle.velocity =(w*particle.velocity+c1*r1*(particle.best_position-particle.position)+c2*r2+(swarm_best_position-particle.position)) #New Position particle.position += particle.velocity #Evaluate Fitness fitness = ObjF(particle.position) #Update PBest if fitness<particle.best_fitness: particle.best_fitness=fitness particle.best_position=particle.position #Update GBest if fitness<swarm_best_fitness: swarm_best_fitness=fitness swarm_best_position=particle.position return swarm_best_position,swarm_best_fitness #Define ObjFunction def F1(x): return np.sum(x**2) def F2(x): return np.max(np.abs(x)) Objective_Function ={'F1':F1,'F2':F2} #Parameters Pop_Size=100 MaxT=100 D=2 # Iterate over each objective function and run PSO for funName, ObjF in Objective_Function.items(): Output = "Running Function = " + funName + "\n" best_position,best_fitness = PSO(ObjF,Pop_Size,D,MaxT) Output += "BEST POSITION : " + str(best_position)+"\n" Output += "BEST COST : " + str(best_fitness) Output += "\n" messagebox.showinfo("PSO RUN",Output)



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