# Equation with multiple variables

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.

equals:

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!

• second equation has delta F instead of delta f (?) Jul 17, 2018 at 13:58
• Yeah, sorry! F stands for large Fee, f for small fee. (F>f) Jul 17, 2018 at 13:59
• 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. Jul 17, 2018 at 14:00
• Yes, these represents the products of the three variables. Thanks! Jul 17, 2018 at 14:01
• 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. Jul 17, 2018 at 14:06

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.

• 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! Jul 17, 2018 at 15:18