R = 10.;
n = 20;
[Lambda] = 10.;
X = RandomReal[{-R, R}, {n, 2}];
F = RandomVariate[ExponentialDistribution[1], n];

[Gamma] = 0.1;
[Tau] = 0.5;
yy = {x, y};
[Beta] = 3.;
ell = x [Function] (x)^-[Beta];
NN = 10^-12 8000^[Beta];

r = Table[F[[i]] ell[Norm[yy - X[[i]]]], {i, 1, n}];
s = Table[ Log[r[[i]]/([Gamma] Total[Delete[r, i]] + NN)], {i, 1, n}];
Show[
 Table[
  RegionPlot[
   s[[i]] >= Log[[Tau]],
   {x, -R, R}, {y, -R, R},
   MaxRecursion -> 5,
   PlotPoints -> 20,
   PlotStyle -> {FaceForm[{Opacity[0.5], ColorData[97][i]}]},
   BoundaryStyle -> ColorData[97][i]
   ],
  {i, 1, n}],
 Graphics[Point[X]]
 ]