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Exponent optimization with constrains

Posted 11 years ago

Hello, I'm trying to find an optimization for each player (each one has a utilitiy function) with constraints. the problem has an exponent factor. I don't know how to construct the problem in mathematica and to find a feasible solution for each player (or potentialy an equilibrium).

Thanks!

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POSTED BY: yossi sh
5 Replies
Posted 11 years ago
POSTED BY: Bill Simpson
Posted 11 years ago

I think that Za and Zb should be maximized seperately. Is this what you've wrote?

POSTED BY: yossi sh
Posted 11 years ago
POSTED BY: Bill Simpson
Posted 11 years ago

0<=Pa<=1, 0<=Pb<=1

POSTED BY: yossi sh
Posted 11 years ago

Can you provide any additional constraint information?

In[1]:= s = 95;
u = 0.1;
x = 100;
k = 0.01;
Subscript[c, A] = (Subscript[p, A]*(s*(1 + u) - x)) + k;
Subscript[c, B] = (Subscript[p, B]*(s*(1 + u) - x)) - k;
Subscript[Z, A]=(1-(v-Subscript[c,A])/(Subscript[c,B]-Subscript[c,A]))^\[Beta] (v-Subscript[c,A]) ;
Subscript[Z, B]=(1-(v-Subscript[c,B])/(Subscript[c,B]-Subscriipt[c,B]-v);
Maximize[{Norm[Subscript[Z, A]] + Norm[Subscript[Z, B]], Subscript[c, A] <= v <= Subscript[c, B]},
   {v, \[Alpha], \[Beta], Subscript[p, A], Subscript[p, B]}]

During evaluation of In[61]:=NMaximize::cvdiv:Failed to converge to a solution. The function may be unbounded.

Out[68]= {1.945590892669753*10^514, {v -> -48.2786, \[Alpha] -> 56.0364, \[Beta] -> -102.072,
   Subscript[p, A] -> -52.0972, Subscript[p, B] -> -10.7259}}
POSTED BY: Bill Simpson
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