Slide 34
Slide 34 text
Nonlocal Mean Field Game System
t
+ H(x, r ) = f0 (t, x, ⇢(x, t)) + f1
✓
t, x,
Z
⌦
K(x, y)⇢(y, t)dy
◆
⇢t
r · (⇢r
pH(x, r )) = 0
⇢(x, 0) = ⇢0(x), (x, 1) = g0 (x, ⇢(x, 1)) + g1
✓
x,
Z
⌦
S(x, y)⇢(y, 1)dy
◆
I
Initial-terminal conditions:
⇢0(x), g0 (x, ⇢(x, 1)) + g1 x,
R
⌦ S(x, y)⇢(y, 1)dy
I
Unknowns: ⇢, : ⌦ ⇥ [0, 1] ! R
I
Nonlocal interactions: f1 x,
R
⌦ K(x, y)⇢(y, t)dy
I
Local interactions: f0 (t, x, ⇢(x, t))
3
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