https://www.nicovideo.jp/watch/sm34787886 https://youtu.be/ko0ILd2wyWw

2. “Vengeance Is Sweet.”
— Severus Snape —

5. p1, p2
πi(pi) =
piq − cq, pj > pi ≥ c
pi
q
2
− c
q
2
, pi = pj ≥ c
0, pi > pj ≥ c
↓ q = 100 − pi

6. πi(pi) =
piq − cq, pj > pi ≥ c
pi
q
2
− c
q
2
, pi = pj ≥ c
0, pi > pj ≥ c
p1 > p2 > c
π2(p2) = p2q − cq
π1(p1) = 0 p1 = p2 − e

7. p2 > p1 > c
π2(p2) = 0
π1(p1) = p1q − cq
p2 = p1 − e
πi(pi) =
piq − cq, pj > pi ≥ c
pi
q
2
− c
q
2
, pi = pj ≥ c
0, pi > pj ≥ c

8. p1 = p2 = p > c
π2(p2) = p
q
2
− c
q
2
π1(p1) = p
q
2
− c
q
2
πi(pi) =
piq − cq, pj > pi ≥ c
pi
q
2
− c
q
2
, pi = pj ≥ c
0, pi > pj ≥ c
p1 = p − e

9. p1 = p2 = p = c
π2(p2) = p
q
2
− c
q
2
π1(p1) = p
q
2
− c
q
2
πi(pi) =
piq − cq, pj > pi ≥ c
pi
q
2
− c
q
2
, pi = pj ≥ c
0, pi > pj ≥ c

10. p1 = p2 = p = c
π2(p2) = p
q
2
− c
q
2
= 0
π1(p1) = p
q
2
− c
q
2
= 0
πi(pi) =
piq − cq, pj > pi ≥ c
pi
q
2
− c
q
2
, pi = pj ≥ c
0, pi > pj ≥ c

11. Q = 100 − P
Q = P
Q = 100 − P
P = 20
200
3 Q = 100 − P
Q = P
100
3
200
3
Q = 100 − P
P = 20
160
3
140
3
Q = 100 − P
Q = P
100
3
200
3
Q = 100 − P
P = 20
Q = 100 − P
P = 20
60
40

12.
p = p * > c
p * p = p *
p = c

13. p = p * ( > c)
p *
p * = 60, c = 20
πi(p*) = p *
q
2
− c
q
2
= 60 *
40
2
− 20 *
40
2
= 800 = π*
↓ q = 100 − pi
p *
π *
π *
p * −e
p * c
? ?
c
p *
p *
π *
π *

14. p = p * −1
p *
p *
π *
π *
p * −e
p * c
? ?
c
p *
p *
π *
π *
π′
0
π1(p * −1) = (p * −1)q − cq = 59 * 41 − 20 * 41 = 1599 = π′( ≓ 2π*)

15. p = p * −1
p *
p *
π *
π *
p * −e
p * c
? ?
c
p *
p *
π *
π *
π′
0
0
0
0
0
π1(p * −1) = (p * −1)q − cq = 59 * 41 − 20 * 41 = 1599 = π′( ≓ 2π*)

16. π *
π *
π * π *
π * π *
2π *
π * π * π * π *
0 0 0 ⋯
⋯
π * <
δ
1 − δ
π * ⇔
1
2
< δ

17. See you next time