A simplified version of my problem is:

z=5
y=6
a + b == z
c + d  == y

Gb[x_] = UnitStep[x - 1] + 2*UnitStep[x - 2] + UnitStep[x - 3] +  2*UnitStep[x - 4]
Gg[x_]= UnitStep[x] - UnitStep[x - 3]
Gs[x_]= 5*UnitStep[x] - UnitStep[x - 1] - 2*UnitStep[x - 2] -    2*UnitStep[x - 4]

wwa[x_] = Max[0, Gs[x] - (y - c)];
wwb[x_] = Max[0, Gs[x] - wwa[x] - (y - c - d)];

wwc[x_] = Gb[x] - Max[0, Gb[x] - c];
wwd[x_] = Gb[x] - wwc[x] - Max[0, Gb[x] - wwc[x] - d];

wwe[x_] = y - wwc[x] - wwa[x];
wwf[x_] = y - wwd[x] - wwb[x];

myfunction[x_] = a*c + 1.5 b d -4 Integrate[wwd, {x, 0, a }] +
      5 Integrate[wwb, {x, 0, a }] +  3 Integrate[wwf, {x, 0, a }] - 
      6 Integrate[wwc, {x, a, a+b }] + 6 Integrate[wwa, {x, a, a+b }] + 
      4 Integrate[wwe, {x, a, a+b }] 

a and b shall try to maximize the value of myfunction; c and d shall try to minimize the value of myfunction:

It can be seen as a Zero-sum game and its about to find the Nash-Equilibrum: Lets say Player A tries to Maximize his wins (=the value of myfunction) with his parameters a and b whereas Player B tries to Minimize his losses (=the value of myfunction) with his parameters c and d.
Minimax algorhythms are usually used for that, ( i already found one at https://reference.wolfram.com/language/tutorial/ConstrainedOptimizationLocalNumerical.html , but havent been able to use it on my problem)

Do you guys know how to use Mathematica to solve that problem?

Regards, Steve