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symbolic_am_solution.m
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%*************************************************************
%% ccc game
%*************************************************************
clc
clear
!rm symbolic_am_solution.txt;
diary symbolic_am_solution.txt;
fprintf('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n');
fprintf('Solving the alternativ move game\n')
fprintf('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n');
fprintf('\n');
fprintf('-----------------------------------------------\n')
fprintf('Solving the ccc game\n')
fprintf('-----------------------------------------------\n')
fprintf('AI1v = r1-Kc + bet*pc*H11+bet*(1-pc)*tpm11*logsumK\n');
fprintf('AI1x= r1 + bet*pc*H12+bet*(1-pc)*tpm12*logsumK\n');
fprintf('Bij=beta*(1-pc)*tpmij\n');
syms AI1x AI1v B11 B21 B12 B22 v11 x11
S1_ccc = solve( ...
v11==AI1v+(B11*v11+B21*x11), ...
x11==AI1x+(B12*v11+B22*x11), ...
x11, v11)
v11_ccc=S1_ccc.v11
x11_ccc=S1_ccc.x11
diary off;
return
S1_ccc = solve( ...
CN1== AN1 + B*P2 *(P1*CI1+(1-P1)*CN1) ...
+ B*(1-P2)*(P1*CI1+(1-P1)*CN1), ...
CI1== AI1 + B*P2 *(P1*CI1+(1-P1)*CN1) ...
+B*(1-P2)*(P1*CI1+(1-P1)*CN1), ...
CN1,CI1);
CN1_ccc=S1_ccc.CN1
CI1_ccc=S1_ccc.CI1
%*************************************************************
%% c1cc game
%*************************************************************
fprintf('-----------------------------------------------\n')
fprintf('Solving the c1cc game - SIMPLIFIED VERSION\n')
fprintf('-----------------------------------------------\n')
fprintf('B=beta*(1-pc)\n');
fprintf('AN1=EPN1+beta*pc*(P2*hC1+(1-P2)*hC1)\n');
fprintf('AI1=EPI1 +beta*pc*(P2*hC1_ccc+(1-P2)*hC1_ccc)\n');
fprintf(' + B*P2 *(P1_ccc *CI1_ccc +(1-P1_ccc) *CN1_ccc ) \n');
fprintf(' + B*(1-P2)*(P1_ccc*CI1_ccc+(1-P1_ccc) *CN1_ccc) \n');
syms AI1 AN1 B P1 P2 CI1 CN1 ...
P1_ccc CI1_ccc CN1_ccc;
S1_c1cc = solve( ...
CN1== AN1 + B*P2 *(P1*CI1+(1-P1)*CN1) ...
+ B*(1-P2)*(P1 *CI1 +(1-P1) *CN1 ), ...
CI1== AI1 , ...
CN1,CI1);
CN1_c1cc=S1_c1cc.CN1
CI1_c1cc=S1_c1cc.CI1
%*************************************************************
%% cc2c game
%*************************************************************
fprintf('-----------------------------------------------\n')
fprintf('Solving the cc2c game - SIMPLIFIED VERSION \n')
fprintf('-----------------------------------------------\n')
fprintf('AN1=EPN1+beta*pc*(P2*hC1_ccc+(1-P2)*hC1)\n');
fprintf(' + B*P2 *(P1_ccc*CI1_ccc+(1-P1_ccc)*CN1_ccc)\n');
fprintf('AI1=EPI1 +beta*pc*(P2*hC1_ccc+(1-P2)*hC1)\n');
fprintf(' + B*P2*(P1_ccc *CI1_ccc+(1-P1_ccc)*CN1_ccc)\n');
fprintf('B=beta*(1-pc)\n');
syms AI1 AN1 B P1 P2 CI1 CN1 ...
P1_ccc CI1_ccc CN1_ccc;
S1_cc2c = solve( ...
CN1== AN1 + B*(1-P2)*(P1*CI1+(1-P1)*CN1), ...
CI1== AI1 + B*(1-P2)*(P1*CI1+(1-P1)*CN1), ...
CN1,CI1);
CN1_cc2c=S1_cc2c.CN1
CI1_cc2c=S1_cc2c.CI1
%*************************************************************
%% c1c2c game - SIMPLIFIED VERSION
%*************************************************************
fprintf('-----------------------------------------------\n')
fprintf('Solving the c1c2c game - SIMPLIFIED VERSION\n')
fprintf('-----------------------------------------------\n')
fprintf('B=beta*(1-pc)\n');
fprintf('AN1=EPN1+beta*pc*(P2*hC1_c1cc+(1-P2)*hC1)\n');
fprintf(' +B*P2*(P1_c1cc*CI1_c1cc+(1-P1_c1cc)*CN1_c1cc)\n\n');
fprintf('AI1=EPI1 +beta*pc*(P2*hC1_ccc+(1-P2)*hC1_cc2c)\n')
fprintf(' + B*P2 *(P1_ccc *CI1_ccc +(1-P1_ccc) *CN1_ccc )\n');
fprintf(' + B*(1-P2)*(P1_cc2c*CI1_cc2c+(1-P1_cc2c) *CN1_cc2c)\n')