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 ...
Learn Pelican Optimization Algorithm Code Implementation Step-By-StepPOA-CODE Video Chapters:00:00 Introduction01:22 Test Function Information Program File02:37 Pelican Optimization Algorithm Program File11:23 Main Program File12:30 Conclusion
1.) Test Function Information File
function [LB,UB,D,FitF] = test_fun_info(C)
switch C
case 'F1'
FitF = @F1;
LB=-100;
UB =100;
D =30;
case 'F2'
FitF = @F2;
LB=-10;
UB =10;
D =30;
case 'F3'
FitF = @F3;
LB=0;
UB=1;
D=3;
end
end
% F1
function R = F1(x)
R=sum(x.^2);
end
% F2
function R = F2(x)
R=sum(abs(x))+prod(abs(x));
end
2.) POA File
function[Best_Solution,Best_Location,Sol_con_Curve]=POA(PopSize,MaxT,LB,UB,D,FitF)
LB=ones(1,D).*(LB); % Lower limit
UB=ones(1,D).*(UB); % Upper limit
% POPULATION INITIALIZATION PHASE
for i=1:D
X(:,i) = LB(i)+rand(PopSize,1).*(UB(i) - LB(i)); % Initial population
end
% FITNESS VALUES CALCULATION
for i =1:PopSize
L=X(i,:);
FitnessVal(i)=FitF(L);
end
%%
for t=1:MaxT
%% update the best condidate solution
[Best_Agent_Val , Best_Agent_Loc]=min(FitnessVal);
if t==1
Best_Pos=X(Best_Agent_Loc,:); % Optimal location
Best_Val=Best_Agent_Val; % The optimization objective function
elseif Best_Agent_Val<Best_Val
Best_Val=Best_Agent_Val;
Best_Pos=X(Best_Agent_Loc,:);
end
%% UPDATE location of food
Agents_Target=[];
g=randperm(PopSize,1);
Agents_Target=X(g,:);
Agents_Target=FitnessVal(g);
%%
for i=1:PopSize
%% PHASE 1: Moving towards prey (exploration phase)
I=round(1+rand(1,1));
if FitnessVal(i)> Agents_Target
New_Pos=X(i,:)+ rand(1,1).*(Agents_Target-I.* X(i,:)); %Eq(4)
else
New_Pos=X(i,:)+ rand(1,1).*(X(i,:)-1.*Agents_Target); %Eq(4)
end
New_Pos= max(New_Pos,LB);
New_Pos = min(New_Pos,UB);
% Updating X_i using (5)
New_Fit = FitF(New_Pos);
if New_Fit <= FitnessVal(i)
X(i,:) = New_Pos;
FitnessVal(i)=New_Fit;
end
%% END PHASE 1: Moving towards prey (exploration phase)
%% PHASE 2: Winging on the water surface (exploitation phase)
New_Pos=X(i,:)+0.2*(1-t/MaxT).*(2*rand(1,D)-1).*X(i,:);% Eq(6)
New_Pos= max(New_Pos,LB);
New_Pos = min(New_Pos,UB);
% Updating X_i using (7)
New_Fit = FitF(New_Pos);
if New_Fit <= FitnessVal(i)
X(i,:) = New_Pos;
FitnessVal(i)=New_Fit;
end
%% END PHASE 2: Winging on the water surface (exploitation phase)
end
best_so_far(t)=Best_Val;
average(t) = mean (FitnessVal);
end
Best_Solution=Best_Val;
Best_Location=Best_Pos;
Sol_con_Curve=best_so_far;
end
3.) Main File
clc
clear all
%Test Function
Test_Fun='F3';
% Total Number of Pelicans
PopSize=50;
% Maximum number of iteration
MaxT=500;
% Test Function Details
[LB,UB,D,FitF]=test_fun_info(Test_Fun);
% POA Calculation
[BestVal,BestLoc,Sol_con_Curve]=POA(PopSize,MaxT,LB,UB,D,FitF);
subplot(1,1,1);
semilogy(Sol_con_Curve,'Color','r');
title('Convergence Curve');
xlabel('Iteration');
ylabel('Best Value');
axis tight
grid on
box on
legend ('POA')
% Display Solution
display(['Best Position' [num2str(Test_Fun)],' = ', num2str(BestLoc)]);
display(['Best Solution' [num2str(Test_Fun)],' = ', num2str(BestVal)]);
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