https://www.nicovideo.jp/watch/sm33118075 https://www.youtube.com/watch?v=DNXGJtIU6jE&t=616s

2. “Left or right ”

4. A B

5. A B
A B

6. A B

7. A B

8. A B
:EA(p)=pq×0+p(1-q)×1+(1-p)q×1+(1-p)(1-q)×0
=p(1-q)+(1-p)q
=(1-2q)p+q

9. A B
:EB(q)=pq×1+p(1-q)×0+(1-p)q×0+(1-p)(1-q)×1
=pq+(1-p)(1-q)
=(2p-1)q+1-p

10. A B
:EA(p)=(1-2q)p+q
0≦q<1/2 , p=1 1-2q>0
q=1/2 , p 0≦p≦1)
1/2<q≦1 , p=0 1-2q<0
:EB(q)=(2p-1)q+1-p
0≦p<1/2 , q=0 2p-1<0
p=1/2 , q 0≦q≦1)
1/2<p≦1 , q=1 2p-1>0

11. :EA(p)=(1-2q)p+q
0≦q<1/2 , p=1 1-2q>0
q=1/2 , p 0≦p≦1)
1/2<q≦1 , p=0 1-2q<0
:EB(q)=(2p-1)q+1-p
0≦p<1/2 , q=0 2p-1<0
p=1/2 , q 0≦q≦1)
1/2<p≦1 , q=1 2p-1>0

12. :EA(p)=(1-2q)p+q
0≦q<1/2 , p=1 1-2q>0
q=1/2 , p 0≦p≦1)
1/2<q≦1 , p=0 1-2q<0
:EB(q)=(2p-1)q+1-p
0≦p<1/2 , q=0 2p-1<0
p=1/2 , q 0≦q≦1)
1/2<p≦1 , q=1 2p-1>0
1. ((p,1-p),(q,1-q))=((1/2,1/2),(1/2,1/2))
=>
2. (pure strategy)
(mixed strategy)
3.
=>

13. :EA(p)=(1-2q)p+q
0≦q<1/2 , p=1 1-2q>0
q=1/2 , p 0≦p≦1)
1/2<q≦1 , p=0 1-2q<0
:EB(q)=(2p-1)q+1-p
0≦p<1/2 , q=0 2p-1<0
p=1/2 , q 0≦q≦1)
1/2<p≦1 , q=1 2p-1>0
1.
=>

16. A B
,

17. A B

18. A B
:EA(p)=pq×1+p(1-q)×(-1)+(1-p)q×2+(1-p)(1-q)×0
=-p+2q ≦ 2q = EA(0)

19. A B
:EB(q)=pq×1+p(1-q)×2+(1-p)q×(-1)+(1-p)(1-q)×0
=-q+2p ≦ 2p = EB(0)

20. A B
((p,1-p),(q,1-q))=((0,1),(0,1))

21. See you next time