paramsubs = {b1 -> 0, b2 -> 0, b3 -> 1/3, e3 -> 1/200616, 
        e4 -> 1/235464, e5 -> 1/1182264}
 
set_yy_approx = {0.05735701, 0.0608687, 0.06634303, 0.07704447, 0.10034813, 0.10340788, 0.05574581, 0.10034813, 0.10034004, 0.34082523, 0.31834698, 0.34082543, 0.31834728, 0.34082523, 0.34082512, 0.34082208, 0.31834426, 0.34082261, 0.31834426, 0.34082262, 0.34082214}
  
varibs = {a1f2 -> 0.05735701, a1f3 -> 0.0608687, 
a2f1 -> 0.05735701, a2f3 -> 0.0608687, a3f1 -> 0.06634303, a3f2 -> 0.06634303, a12 -> 0.07704447, a13 -> 0.10034813, a21 -> 0.07704447, a23 -> 0.10034813, a31 -> 0.10340788, a32 -> 0.10340788, af21 -> 0.05574581, af23 -> 0.10034813, af32 -> 0.10034004, af13 -> 0.10034813, af31 -> 0.10034004, af12 -> 0.05574581, u2b1r23 -> 0.34082523, 
u3b2r31 -> 0.31834698, u1b3r12 -> 0.34082543, 
u1b2r13 -> 0.34082523, u3b1r32 -> 0.31834698, 
u2b3r21 -> 0.34082543, u3b12r3 -> 0.31834728, 
u1b23r1 -> 0.34082523, u2b31r2 -> 0.34082512, 
u3b21r3 -> 0.31834728, u2b13r2 -> 0.34082523, 
u1b32r1 -> 0.34082512, u2b12r3 -> 0.34082208, 
u3b23r1 -> 0.31834426, u1b31r2 -> 0.34082261, 
u1b21r3 -> 0.34082208, u3b13r2 -> 0.31834426, 
u2b32r1 -> 0.34082261, u3b1r23 -> 0.31834426, 
u1b2r31 -> 0.34082262, u2b3r12 -> 0.34082214, 
u3b2r13 -> 0.31834426, u2b1r32 -> 0.34082262, 
u1b3r21 -> 0.34082214}

shapval = {7/18, 7/18, 2/9} 
shapval_decimal = {0.38888888, 0.38888888, 0.22222222}
nuke = {1/3, 1/3, 1/3}

payoffs_approx = {0.34082191, 0.34082191, 0.31834372}
payoffs_total = 0.99998756

payoffs_normalized = {0.34082615, 0.34082615, 0.31834768}
npay_rational_approx = {91/267, 91/267, 85/267}