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GAMS_tables_example.gms
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GAMS_tables_example.gms
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SETS
h heath / 1*4 /
l liver quality / 1*5 /
k rank /1*10/
a action /0,1/
y signal /1*4/
i Grid Vectors /1*10/;
Alias
(h,h1)
(k,k1)
(k,k2)
(k,k3)
(l,l1)
(y,y1)
(i,i1);
SCALAR lambda daily discount rate;
lambda = 0.999917;
PARAMETERS
Pi(i,k) Grid Vectors
pi_prime(k) updated Pi's
v(h,l,i) value
v2(h,l,i) value after one iteration
vwait value if action is wait
x(h,l,i) policy
r_TS(h,l) scaled rewards;
TABLE pH(h,h1) health probability matrix H{h'|h}
1 2 3 4
1 0.9966 0.0032 0.0000 0.0000
2 0.0005 0.9973 0.0015 0.0000
3 0.0000 0.0031 0.9872 0.0066
4 0.0000 0.0001 0.0056 0.9672;
Table pK(k,k1) rank transition probability matrix K{k'|k}
1 2 3 4 5 6 7 8 9 10
1 0.906080 0.079090 0.009077 0.003055 0.000933 0.000402 0.000239 0.000420 0.000390 0.000315
2 0.116973 0.667786 0.172183 0.032105 0.007551 0.001527 0.000647 0.000293 0.000432 0.000501
3 0.011606 0.135391 0.612947 0.207797 0.023907 0.004910 0.001718 0.000709 0.000306 0.000709
4 0.002600 0.015762 0.121602 0.661372 0.173916 0.016546 0.004873 0.001717 0.000638 0.000973
5 0.000437 0.003196 0.012090 0.138476 0.654926 0.162426 0.018533 0.006169 0.002334 0.001414
6 0.000151 0.000790 0.002530 0.012178 0.135785 0.639100 0.178318 0.020798 0.008078 0.002273
7 0.000110 0.000342 0.000692 0.003027 0.012824 0.133141 0.636736 0.183712 0.024584 0.004831
8 0.000000 0.000149 0.000337 0.000883 0.003207 0.011691 0.126562 0.649365 0.196324 0.011483
9 0.000000 0.000000 0.000123 0.000217 0.000525 0.001624 0.005919 0.060759 0.813604 0.117228
10 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000251 0.006670 0.993079;
Table pL(k1,l1) liver offer probability matrix L{l'|k'}
1 2 3 4 5
1 0.275539 0.099973 0.079724 0.027113 0.517651
2 0.233531 0.088320 0.074426 0.025662 0.578061
3 0.198184 0.078081 0.069496 0.024292 0.629946
4 0.153442 0.064411 0.062422 0.022291 0.697435
5 0.105600 0.048642 0.053384 0.019668 0.772706
6 0.066193 0.034243 0.043904 0.016818 0.838841
7 0.036239 0.021756 0.034079 0.013729 0.894197
8 0.015531 0.011474 0.023806 0.010297 0.938892
9 0.002524 0.002750 0.010197 0.005166 0.979364
10 0.000004 0.000011 0.000149 0.000112 0.999724;
Table pO(k1,y1) O{y'|k'}
1 2 3 4
1 0.000000 0.000000 0.000011 0.999989
2 0.000000 0.000000 0.001965 0.998035
3 0.000000 0.000000 0.025417 0.974583
4 0.000000 0.000000 0.169813 0.830187
5 0.000000 0.000000 0.581631 0.418369
6 0.000000 0.000000 0.941542 0.058458
7 0.000000 0.000038 0.999240 0.000722
8 0.000000 0.026563 0.973437 0.000000
9 0.000000 0.436372 0.563628 0.000000
10 0.402496 0.596228 0.001276 0.000000;
Table pM(h,k) M{k|h}
1 2 3 4 5 6 7 8 9 10
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000
2 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000583 0.034604 0.964813
3 0.000000 0.000000 0.000545 0.008589 0.044163 0.100029 0.151116 0.217229 0.441159 0.037169
4 0.176032 0.131834 0.173449 0.269227 0.201257 0.046620 0.001581 0.000000 0.000000 0.000000;
Table r_t(h,l) unscaled reward r_T{h l}
1 2 3 4
1 2233 1985 1837 1645
2 1992 1785 1647 1485
3 1754 1577 1465 1325
4 1517 1373 1277 1135;
r_TS(h,l) = (1-lambda**(r_T(h,l)+1))/(1-lambda);