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I'm totally new at Mathematica, but I'm stuck with my thesis. I'm trying to solve the following equation with multiple variavles for v, with all variables between 0 and 1, F is larger than f and with p smaller than k.

enter image description here

equals:

enter image description here

So I'm trying to solve it by doing:

Solve[δ*f+γ*α*(1-β)/(α*(1-β)+(1-α)*(1-β)*(1-v))==(β+(1-β)*v)(c/((1-α)*(1-β)*v*(p-k)^2)(δ*F+γ*α*β/(α*β+(1-α)*(β+(1-β)*v))+(1-c/((1-α)*(1-β)*v*(p-k)^2))γ*α)),v] 

However, not surprisingly, I do not get any results. I don't really know what I have to do now.. Could someone tell me what to do?

Thanks!

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  • $\begingroup$ second equation has delta F instead of delta f (?) $\endgroup$
    – chris
    Jul 17, 2018 at 13:58
  • $\begingroup$ Yeah, sorry! F stands for large Fee, f for small fee. (F>f) $\endgroup$
    – B.1993
    Jul 17, 2018 at 13:59
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    $\begingroup$ Did you mean γαβ to represent the product of three variables? The way you have it, it's a single variable with a three letter name. Put space or * between them to multiply symbols. $\endgroup$
    – John Doty
    Jul 17, 2018 at 14:00
  • $\begingroup$ Yes, these represents the products of the three variables. Thanks! $\endgroup$
    – B.1993
    Jul 17, 2018 at 14:01
  • $\begingroup$ I do get a result just takes a long time and it is absurdly long. Could be making mistakes as I am unsure whether \[Delta]f is two symbols or one. Same in a couple more places. Can you plug in numerical values before evaluating that would speed things up considerably. $\endgroup$ Jul 17, 2018 at 14:06

1 Answer 1

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An extended comment, not an answer. Look at

\[Delta]*f + \[Gamma]*\[Alpha]*(1 - \[Beta])/(\[Alpha]*(1 - \[Beta]) \
+ (1 - \[Alpha])*(1 - \[Beta])*(1 - v)) - (\[Beta] + (1 - \[Beta])*
       v) (c/((1 - \[Alpha])*(1 - \[Beta])*v*(p - k)^2) (\[Delta]*
         F + \[Gamma]*\[Alpha]*\[Beta]/(\[Alpha]*\[Beta] + (1 - \
\[Alpha])*(\[Beta] + (1 - \[Beta])*v)) + (1 - 
           c/((1 - \[Alpha])*(1 - \[Beta])*
              v*(p - k)^2)) \[Gamma]*\[Alpha])) // 
  Together // Numerator

obtained by subtracting the right side from the left and taking the numerator of the resulting rational function. I don't show the huge result. Solve is attempting to find the zeros of this monstrosity. The roots will be even more monstrous. What are you trying to accomplish here? A symbolic result exists, but will be incomprehensible and slow to evaluate. Substituting numbers for symbolic parameters and using NSolve or FindRoot to get numeric answers may be more practical.

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  • $\begingroup$ I was trying to find one or multiple values of v, for which a game theoretical equilibrium could exist. So therefore I needed to have a value of v for which both the left hand side and the right hand side of the equation are equal (These functions represent micro-economic utility functions for a certain strategy). But looking at these outcomes, I don't think this will be doable right now (for me). Thanks for the help anyways! $\endgroup$
    – B.1993
    Jul 17, 2018 at 15:18

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