I know this is a rookie question but its been years since I've used MatLab. I need to use p_r,p_p,p_s to calculate p_rn,p_pn,p_sn and then use those values in place of p_r,p_p,p_s in subsequent calculations and then store them all in a matrix.

I believe I should be using a for loop with the definition of the matrix inside but the details have escaped me. Any help with this would be greatly appreciated. I would like to end up with something like this: A 101x3 matrix

    [p_r,  p_p,  p_s;
     p_rn1,  p_pn1,  p_sn1;
     p_rn2,  p_pn2,  p_sn2;
    ...;
    p_rn100,  p_pn100,  p_sn100]

___________________________________________________________________________________

    p_r = 0.35;
    p_p = 0.33;
    p_s = 0.32;

    T_0 = 0.39;
    T_1 = 0.23;
    T_2 = 0.38;

    W_0 = 0.50;
    W_1 = 0.29;
    W_2 = 0.21;

    L_0 = 0.35;
    L_1 = 0.38;
    L_2 = 0.27;

    p_rn = (((p_r)^2)*(T_0)) + (((p_p)^2)*(T_1)) + (((p_s)^2)*(T_2)) + ((p_r)*(p_p)*((L_0)+(W_1))) + ((p_r)*(p_s)*((L_2)+(W_0))) + ((p_p)*(p_s)*((L_1)+(W_2)));

    p_pn = (((p_r)^2)*(T_2)) + (((p_p)^2)*(T_0)) + (((p_s)^2)*(T_1)) + ((p_r)*(p_p)*((L_2)+(W_0))) + ((p_r)*(p_s)*((L_1)+(W_2))) + ((p_p)*(p_s)*((L_0)+(W_1)));

    p_sn = (((p_r)^2)*(T_1)) + (((p_p)^2)*(T_2)) + (((p_s)^2)*(T_0)) + ((p_r)*(p_p)*((L_1)+(W_2))) + ((p_r)*(p_s)*((L_0)+(W_1))) + ((p_p)*(p_s)*((L_2)+(W_0)));

[per isakson]

Read this carefully for, Execute statements specified number of times

[Jarrett White]

Trust me, I read that along with many other MatLab articles before I asked a question on here. This is just an effort to seek some insight from someone who could just get me started in the right direction.

Answer 1

[per isakson]

The comment caused me to deleted my first answer.

Caveat: I know next to nothing about Game Theory

Assumption: The expressions in the question define how the probabilities, P(n), are calculated based on their previous values, P(n-1). If so, no recursion is needed.

Try

    >> P = cssm( 1/3+randn(1,3)/200 ); P(1:5,:)
    ans =
        0.3337    0.3273    0.3278
        0.3263    0.3261    0.3252
        0.3186    0.3187    0.3185
        0.3045    0.3045    0.3045
        0.2781    0.2781    0.2781
    >> plot( P )

    >> P = cssm( 1/3+randn(1,3)/200 ); P(1:5,:)
    ans =
        0.3333    0.3410    0.3295
        0.3349    0.3367    0.3359
        0.3383    0.3384    0.3385
        0.3435    0.3435    0.3436
        0.3541    0.3541    0.3541

where

   function    P = cssm(P0)

        P = nan( 101, 3 );  % allocate memory

        p_r = 0.35; p_p = 0.33; p_s = 0.32;
        T_0 = 0.39; T_1 = 0.23; T_2 = 0.38;
        W_0 = 0.50; W_1 = 0.29; W_2 = 0.21;
        L_0 = 0.35; L_1 = 0.38; L_2 = 0.27;

        if nargin == 0
            P(1,:)  = [ p_r, p_p, p_s ];
        else
            P(1,:)  = P0;
        end

        for n = 2 : size( P, 1 )

            P(n,1)  = ((P(n-1,1))^2)*(T_0)                  ... 
                    + ((P(n-1,2))^2)*(T_1)                  ...     
                    + ((P(n-1,3))^2)*(T_2)                  ...
                    + ((P(n-1,1))*(P(n-1,2))*((L_0)+(W_1))) ...
                    + ((P(n-1,1))*(P(n-1,3))*((L_2)+(W_0))) ...
                    + ((P(n-1,2))*(P(n-1,3))*((L_1)+(W_2))) ;

            P(n,2)  = ((P(n-1,1))^2)*(T_2)                  ... 
                    + ((P(n-1,2))^2)*(T_0)                  ...
                    + ((P(n-1,3))^2)*(T_1)                  ...
                    + ((P(n-1,1))*(P(n-1,2))*((L_2)+(W_0))) ...
                    + ((P(n-1,1))*(P(n-1,3))*((L_1)+(W_2))) ...
                    + ((P(n-1,2))*(P(n-1,3))*((L_0)+(W_1))) ;

            P(n,3)  = ((P(n-1,1))^2)*(T_1)                  ...      
                    + ((P(n-1,2))^2)*(T_2)                  ...
                    + ((P(n-1,3))^2)*(T_0)                  ...
                    + ((P(n-1,1))*(P(n-1,2))*((L_1)+(W_2))) ...
                    + ((P(n-1,1))*(P(n-1,3))*((L_0)+(W_1))) ...
                    + ((P(n-1,2))*(P(n-1,3))*((L_2)+(W_0))) ;
        end
    end

[Jarrett White]

Thanks per isakson! What these p_r, p_p, and p_s represent are starting probabilities for strategies in a symmetric zero sum game. I am doing an doing an analysis on conditional responses and the cyclic flow of strategies in discrete time. The p_rn, p_pn, and p_sn, where n=time from 0 to 100, represent the new probabilities of using strategies after each round. So I would like to use p_r to find p_r1, p_r1 to find p_r2, and so on. I guess its a sort of recursive function. Then I need to store these values to construct a plot of their behavior. I'm just not entirely sure of what the correct syntax would be to represent the recursive nature in the loop. I feel like the answer lies in the construction of my definition of p_rn, p_pn, and p_sn.