mx = 200;
vx = 100;
my = 10;
vy = 5;
s = 300;
k = 100;
c = 100;
h = 500;
x = TruncatedDistribution[{0, [Infinity]},
   NormalDistribution[mx, vx]];
y = TruncatedDistribution[{0, [Infinity]},
   NormalDistribution[my, vy]];
f[z_] := PDF[x, z];
F[z_] := CDF[x, z];
g[z_] := PDF[y, z];
G[z_] := CDF[y, z];
eq = Simplify[{W == G[V]*(r + k) + (1 - G[V])*p (s + k),
    V == (1 - F[W])*(p*s - r)}, Assumptions -> {V >= 0, W > 0}];
func[R_?NumericQ, P_?NumericQ] :=
  FindRoot[eq /. {r -> R, p -> P}, {{V, 1/2}, {W, 1/3}}];
H[x_?NumericQ] := NIntegrate[(j - h)*f[j], {j, x, [Infinity]}];
L[P_?NumericQ, x_?NumericQ] :=
  NIntegrate[P*c*g[j], {j, x, [Infinity]}];
NMaximize[{H[Evaluate[(W /. func[r, p])]] -
    L[p, Evaluate[(V /. func[r, p])]], 0 <= r <= p*s,
   0 <= p <= 1}, {r, p}, Method -> "NelderMead",
  WorkingPrecision -> 20] // Quiet
Plot3D[H[F[Evaluate[(W /. func[r, p])]]] -
  L[p, G[Evaluate[(V /. func[r, p])]]], {r, 0, 300}, {p, 0, 1}]