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# Exponent optimization with constrains

Posted 10 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! Attachments:
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Posted 10 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]-Subscript[c,A]))^\[Alpha] (Subscript[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 10 years ago
 0<=Pa<=1, 0<=Pb<=1
Posted 10 years ago
 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]-Subscript[c,A]))^\[Alpha](Subscript[c,B]-v); Maximize[{Norm[Subscript[Z,A]]+Norm[Subscript[Z,B]], Subscript[c,A]<=v<=Subscript[c,B] && 0<=Subscript[p,A]<=1 && 0<=Subscript[p,B]<= 1}, {v, \[Alpha], \[Beta], Subscript[p,A], Subscript[p,B]}] During evaluation of In[1]:=NMaximize::cvdiv:Failed to converge to a solution. The function may be unbounded. Out[9]= {3.97046*10^15, {v -> 0.101697, \[Alpha] -> 53.8285, \[Beta] -> -34.2923, Subscript[p, A] -> 0.0203771, Subscript[p, B] -> 0.0799841}} You may want to look at the values of each part of ZA and ZB to determine whether more constraints are needed or whether there is something about the way that I have done this which is incorrect.
Posted 10 years ago
 I think that Za and Zb should be maximized seperately. Is this what you've wrote?
Posted 10 years ago
 From the initial post I was guessing that you needed to maximize both of the items.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] - Subscript[c, A]))^[Alpha] (Subscript[c, B] - v); Maximize[{Subscript[Z, A], Subscript[c, A] <= v <= Subscript[c, B] && 0 <= Subscript[p, A] <= 1 && 0 <= Subscript[p, B] <= 1}, {v, [Alpha], [Beta], Subscript[p, A],Subscript[p, B]}]During evaluation of In[1]:=NMaximize::nrnum:The function value -0.113773+0.104822 I is not a real number at {v,[Alpha],[Beta],Subscript[p, A],Subscript[p, B]} = {1.24375,0.162408,-0.0367399,0.0548333,0.081051}. >>Out[6]= {0.863531, {v -> 0.754547, [Alpha] -> -0.523666, [Beta] -> -0.734744, Subscript[p, A] -> 0.0000800015, Subscript[p, B] -> 0.906934}}In[7]:= Maximize[{Subscript[Z, B], Subscript[c, A] <= v <= Subscript[c, B] && 0 <= Subscript[p, A] <= 1 && 0 <= Subscript[p, B] <= 1}, {v, [Alpha], [Beta], Subscript[p, A],Subscript[p, B]}]During evaluation of In[7]:=NMaximize::nrnum:The function value 1.613510^8-4.6536810^7 I is not a real number at {v,[Alpha],[Beta],Subscript[p, A],Subscript[p, B]} = {0.377249,18.8636,-19.7831,0.162586,0.150344}. >>Out[7]= {2.99746*10^7, {v -> 0.454771, [Alpha] -> 16.1621, [Beta] -> -15.78, Subscript[p, A] -> 0.187606, Subscript[p, B] -> 0.2869}}