Game theory matlab

Catalog

1. brief introduction

2. Algorithm principle

3. The example analysis

1. Initialization of each parameter

2. Calculated expectation and actual expectation

3. The game process

4. mapping

  Complete code

---

1. brief introduction

         Game theory It's also called game theory (Game Theory) both Modern mathematics A new branch of , It's also Operations research An important subject of .

         Game theory mainly studies the interaction between formulated incentive structures . It is to study phenomena with the nature of struggle or competition Mathematical theory And methods . Game theory considers the prediction behavior and actual behavior of individuals in the game , And study their optimization strategies . Biologists use game theory to understand and predict some results of evolution .

         Game theory has become economics One of the standard analysis tools . In Biology 、 economics 、 international relation 、 Computer science 、 political science 、 Military strategy and many other disciplines are widely used .

         The basic concept includes players 、 action 、 Information 、 Strategy 、 earnings 、 Equilibrium and results . among People in the game 、 Strategy and revenue are the most basic elements . People in the game 、 Actions and results are collectively referred to as The rules of the game .

         Game theory is simply ,A Take measures to affect B act ,B Behavior influence A The decision , The two play back and forth , Finally, a dynamic balance is achieved . Strictly speaking, game theory is just a way to solve problems .

2. Algorithm principle

         Take electric taxis and power stations for example , Suppose that the electric taxi and the power station belong to the same company , The company wants to control the number of taxis in the target area to achieve the expected distribution through the price pricing measures of power station replacement .

         For drivers , There are two costs , One is distance cost d, One is to pay the cost p, The payment cost is the electricity price paid for replacing the battery , We can set up weighting factors a Combine the two to build a utility function , The driver will choose the smallest replacement station of this function to replace the battery , After replacing the battery, the driver usually starts to receive orders around

         For the company , The objective function is the actual distribution of taxis in different regions e And expectation distribution E The sum of absolute differences of , The company influences the driver's choice by adjusting the price , So as to adjust the distribution of drivers in different areas

Model analysis of two-tier game theory

① The first stage , After the charging station calculates the power change request of each electric taxi , According to the optimization objective , Formulate price strategy

② The second stage , The electric taxi selects the target replacement station from all the replacement stations according to its own utility function to replace the battery

③ The first stage and the second stage are carried out alternately , Until equilibrium is reached

Algorithm design steps

3. The example analysis

1. Initialization of each parameter

n=900;% Power exchange demand 
min_price=170;% The price range of electricity exchange 
max_price=230;
A=normrnd(36,5,1,25);% Initial expectations , The average value is 36, The variance of 5 Gaussian distribution of 
E=fix(A); % the 0 Round the direction , Such as ,4.1,4.5,4.8 Round it all 4
% The following is the adjustment according to the demand E Size 
a=sum(E)-n;
A=A-a/25;
E=fix(A);
b=sum(E)-n;
A=A-b/25;
E=fix(A);
a1=0.05;a2=0.95;% Distance cost and change point price weight 
x=rand(n,1).*20000;% Initialize the required vehicle location 
y=rand(n,1).*20000;
H=[2,2;2,6;2,10;2,14;2,18% Initialize the power station location 
6,2;6,6;6,10;6,14;6,18
10,2;10,6;10,10;10,14;10,18
14,2;14,6;14,10;14,14;14,18
18,2;18,6;18,10;18,14;18,18].*1000;
% Draw the location map of the initialized driver and the power station 
figure
plot(x,y,'r*')
hold on
plot(H(:,1),H(:,2),'bo')
legend(' The driver ',' Change station ')
title(' Initial location map ')

return ：

2. Calculated expectation and actual expectation

%%  Calculated expectation and actual expectation 
D=[];% The proportion of demand vehicles to each replacement station 
price=200.*ones(1,25);
for i=1:length(H)
    for j=1:length(x)
            D(i,j)=a1*sqrt((H(i,1)-x(j))^2+(H(i,2)-y(j))^2)+a2*price(i);% The total cost 
    end
end
[d1,d2]=min(D);% Select the nearest replacement station 
C=tabulate(d2(:));% Count the number of power station replacement 
e=C(:,2);
err=sum(abs(E-e')) % Sum of expectation differences , That is, the game object 

return ： Because of the random , All of them may be different every time

3. The game process

%%  game 
J=[]; % The difference between price changes 
ER(1)=err;
for k=2:100
    j=0;
    for i=1:25
        if e(i)<E(i) && price(i)>=min_price
            price(i)=price(i)-1;
            j=j+1;
        end
        if e(i)>E(i) && price(i)<=max_price
            price(i)=price(i)+1;
            j=j+1;
        end
    end
    J=[J,j];
    DD=[];
    for i=1:length(H)
        for j=1:length(x)
            DD(i,j)=a1*sqrt((H(i,1)-x(j))^2+(H(i,2)-y(j))^2)+a2*price(i);
        end
    end
    [dd1,dd2]=min(DD);
    CC=tabulate(dd2(:));
    e=CC(:,2);
    err=sum(abs(E-e'));
    ER=[ER,err];
end

4. mapping

%  mapping 
figure
plot(ER,'-o')
title('E-e The difference of ')
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32])
legend('E-e')

figure
plot(J,'r-o')
title(' The difference in price changes ')
xlabel('Iterations(t)')
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32])
legend('sum of Price(t)-Price(t-1)')

figure
bar(price,0.5)
hold on
plot([0,26],[min_price,min_price],'g--')
plot([0,26],[max_price,max_price],'r--')
title(' The replacement price of the power station ')
ylabel('Price(￥)')
axis([0,26,0,300])
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32]);

figure
h=bar([e,E'],'gr');
set(h(1),'FaceColor','g'); set(h(2),'FaceColor','r');
axis([0,26,0,50])
title(' Expected and actual number of taxis ')
ylabel('E and e')
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32]);
xlabel(' Change station ')
legend('e','E')

return ：

  Complete code

clear;clc;
setenv('BLAS_VERSION','') % Make error correction 
n=900;% Power exchange demand 
min_price=170;% The price range of electricity exchange 
max_price=230;
A=normrnd(36,5,1,25);% Initial expectations , The average value is 36, The variance of 5 Gaussian distribution of 
E=fix(A); % the 0 Round the direction , Such as ,4.1,4.5,4.8 Round it all 4
% The following is the adjustment according to the demand E Size 
a=sum(E)-n;
A=A-a/25;
E=fix(A);
b=sum(E)-n;
A=A-b/25;
E=fix(A);
a1=0.05;a2=0.95;% Distance cost and change point price weight 
x=rand(n,1).*20000;% Initialize the required vehicle location 
y=rand(n,1).*20000;
H=[2,2;2,6;2,10;2,14;2,18% Initialize the power station location 
6,2;6,6;6,10;6,14;6,18
10,2;10,6;10,10;10,14;10,18
14,2;14,6;14,10;14,14;14,18
18,2;18,6;18,10;18,14;18,18].*1000;
% Draw the location map of the initialized driver and the power station 
figure
plot(x,y,'r*')
hold on
plot(H(:,1),H(:,2),'bo')
legend(' The driver ',' Change station ')
title(' Initial location map ')

%%  Calculated expectation and actual expectation 
D=[];% The proportion of demand vehicles to each replacement station 
price=200.*ones(1,25);
for i=1:length(H)
    for j=1:length(x)
            D(i,j)=a1*sqrt((H(i,1)-x(j))^2+(H(i,2)-y(j))^2)+a2*price(i);% The total cost 
    end
end
[d1,d2]=min(D);% Select the nearest replacement station 
C=tabulate(d2(:));% Count the number of power station replacement 
e=C(:,2);
err=sum(abs(E-e')); % Sum of expectation differences , That is, the game object 
% ER(1)=err

%%  game 
J=[]; % The difference between price changes 
ER(1)=err;
for k=2:100
    j=0;
    for i=1:25
        if e(i)<E(i) && price(i)>=min_price
            price(i)=price(i)-1;
            j=j+1;
        end
        if e(i)>E(i) && price(i)<=max_price
            price(i)=price(i)+1;
            j=j+1;
        end
    end
    J=[J,j];
    DD=[];
    for i=1:length(H)
        for j=1:length(x)
            DD(i,j)=a1*sqrt((H(i,1)-x(j))^2+(H(i,2)-y(j))^2)+a2*price(i);
        end
    end
    [dd1,dd2]=min(DD);
    CC=tabulate(dd2(:));
    e=CC(:,2);
    err=sum(abs(E-e'));
    ER=[ER,err];
end
%  mapping 
figure
plot(ER,'-o')
title('E-e The difference of ')
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32])
legend('E-e')

figure
plot(J,'r-o')
title(' The difference in price changes ')
xlabel('Iterations(t)')
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32])
legend('sum of Price(t)-Price(t-1)')

figure
bar(price,0.5)
hold on
plot([0,26],[min_price,min_price],'g--')
plot([0,26],[max_price,max_price],'r--')
title(' The replacement price of the power station ')
ylabel('Price(￥)')
axis([0,26,0,300])
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32]);

figure
h=bar([e,E'],'gr');
set(h(1),'FaceColor','g'); set(h(2),'FaceColor','r');
axis([0,26,0,50])
title(' Expected and actual number of taxis ')
ylabel('E and e')
set(gcf,'unit','normalized','position',[0.2,0.2,0.64,0.32]);
xlabel(' Change station ')
legend('e','E')