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TWEET # Untitled a guest Jun 15th, 2019 67 Never
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1. mx = 200;
2. vx = 100;
3. my = 10;
4. vy = 5;
5. s = 300;
6. k = 100;
7. c = 100;
8. h = 500;
9. x = TruncatedDistribution[{0, [Infinity]},
10.    NormalDistribution[mx, vx]];
11. y = TruncatedDistribution[{0, [Infinity]},
12.    NormalDistribution[my, vy]];
13. f[z_] := PDF[x, z];
14. F[z_] := CDF[x, z];
15. g[z_] := PDF[y, z];
16. G[z_] := CDF[y, z];
17. eq = Simplify[{W == G[V]*(r + k) + (1 - G[V])*p (s + k),
18.     V == (1 - F[W])*(p*s - r)}, Assumptions -> {V >= 0, W > 0}];
19. func[R_?NumericQ, P_?NumericQ] :=
20.   FindRoot[eq /. {r -> R, p -> P}, {{V, 1/2}, {W, 1/3}}];
21. H[x_?NumericQ] := NIntegrate[(j - h)*f[j], {j, x, [Infinity]}];
22. L[P_?NumericQ, x_?NumericQ] :=
23.   NIntegrate[P*c*g[j], {j, x, [Infinity]}];
24. NMaximize[{H[Evaluate[(W /. func[r, p])]] -
25.     L[p, Evaluate[(V /. func[r, p])]], 0 <= r <= p*s,
26.    0 <= p <= 1}, {r, p}, Method -> "NelderMead",
27.   WorkingPrecision -> 20] // Quiet
28. Plot3D[H[F[Evaluate[(W /. func[r, p])]]] -
29.   L[p, G[Evaluate[(V /. func[r, p])]]], {r, 0, 300}, {p, 0, 1}]
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