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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 ...
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Whale Optimization Algorithm Code Implementation || WOA CODE || ~xRay Pixy

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Whale Optimization Algorithm Code Implementation


Whale Optimization Algorithm Code Files


function obj_fun(test_fun)
switch test_fun
    case 'F1'
        x = -100:2:100; y=x;
    case 'F2'
        x = -10:2:10; y=x;
end
end


function [LB,UB,D,FitFun]=test_fun_info(C)
switch C
    case 'F1'
        FitFun = @F1;
        LB = -100; 
        UB = 100;
        D = 30;
    case 'F2'
        FitFun = @F2;
        LB = -10;
        UB = 10;
        D = 30;
end
% F1 Test Function
    function r = F1(x)
        r = sum(x.^2);
    end
% F2 Test Function
    function r = F2(x)
        r = sum(abs(x))+prod(abs(x));
    end
end

function Position = initialize(Pop_Size,D,UB,LB)
SS_Bounds = size(UB,2);

if SS_Bounds == 1
    Position = rand(Pop_Size,D).*(UB-LB)+LB;
end

if SS_Bounds>1
    for i = 1:D
        UB_i = UB(i);
        LB_i = LB(i);
        Position(:,i) = rand(Pop_Size,1).*(UB_i-LB_i)+LB_i; 
    end
end
end

function [Best_Val,Best_Pos,Convergence_Curve]=WOA(Pop_Size,MaxT,LB,UB,D,FitFun)
Best_Pos = zeros(1,D);
Best_Val = inf;

Position = initialize(Pop_Size,D,UB,LB);
Convergence_Curve = zeros(1,MaxT);

T = 0;

while T<MaxT
    for i = 1:size(Position,1)
        CheckUB = Position(i,:)>UB;
        CheckLB = Position(i,:)<LB;
        Position(i,:) = (Position(i,:).*(~(CheckUB+CheckLB)))+UB.*CheckUB+LB.*CheckLB;
        %Calculate Fitness Values
        Fitness_Val = FitFun(Position(i,:));
        %Compare Fitness Values
        if Fitness_Val<Best_Val
            Best_Val = Fitness_Val;
            Best_Pos = Position(i,:);
        end
    end
    a = 2-T*((2)/MaxT);
    a2 = -1+T*((-1)/MaxT);
    
    %Agents Position Update (New Positions)
    for i=1:size(Position,1)
        r1=rand();
        r2=rand();
        A = 2*a*r1-a;
        C = 2 * r2;
        b = 1;
        l = (a2-1)*rand+1;
        p = rand();
        for j = 1:size(Position,2)
            if p<0.5
                if abs(A)>1
                    rand_best_index=floor(Pop_Size*rand()+1);
                    X_rand = Position(rand_best_index,:);
                    D_X_rand = abs(C*X_rand(j)-Position(i,j));
                    Position(i,j) = X_rand(j)-A*D_X_rand;
                elseif abs(A)<1
                    D_Best = abs(C*Best_Pos(j)-Position(i,j));
                    Position(i,j) = Best_Pos(j)-A*D_Best;
                end
            elseif p>=0.5
                distance2Best = abs(Best_Pos(j)-Position(i,j));
                Position(i,j) = distance2Best * exp(b.*1).*cos(1.*2*pi)+Best_Pos(j);    
            end
        end  
    end
    T = T + 1;  %Counter Increment
    Convergence_Curve(T) = Best_Val;
    [T Best_Val]
end
end


clc
clear all
Pop_Size = 100;
Objective_Fun = 'F2';
MaxT = 500;

[LB,UB,D,FitFun] = test_fun_info(Objective_Fun);
[Best_Val,Best_Pos,Sol_Convergence]=WOA(Pop_Size,MaxT,LB,UB,D,FitFun);


subplot(1,1,1);
semilogy(Sol_Convergence,'Color','r');
title('Convergence Curve');
xlabel('Iteration');
ylabel('Best Value');
axis tight
grid on
box on
legend ('WOA')

display(['Best Position',num2str(Best_Pos)]);
display(['Best_Value ',num2str(Best_Val)]);









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