GMT01 - waseda2bun @ ウィキ

GAME01

• Case01

1/2	Left	Middle	Right
UP	(1,0)	(1,2)	(0,1)
DOWN	(0,3)	(0,1)	(2,0)

• 双行列ゲーム (bimatrix game)
• For 1
  • if 2 choose L,U is bette than D.
  • if M,U is bette than D.
  • if R,however,D is bette.
• For 2
  • if 1 choose U,M>R>L
  • if D,L>M>R

1. For 1,neither of two is strictly dominated.
2. For 2,R is strictly dominated by M
3. If 1 know about that and 2 is rational player,we can think case01 like case02

• Case02

1/2	left	Middle
UP	(1,0)	(1,2)
DOWN	(0,3)	(0,1)

In this case,

• For 1
  • if 2 choose L,U is bette than D.
  • if M,U is bette than D.

• For 2
  • if 1 choose U,M>L
  • if D,L>M

1. For 2,neither of two is strictly dominated.
2. For 1,D is strictly dominated by U.
3. If 2 know that 1 know that 2 is rational,then 2 eliminate D,like case 03

• Case03

1/2	left	Middle
UP	(1,0)	(1,2)

So,(U,M)is the outcome of this game.

GAME02

1/2	L	C	R
T	0,4	4,0	5,3
M	4,0	0,4	5,3
B	3,5	3,5	6,6

• for 1
  • if 2 were to play L,M>B>T
  • if C,T>B>M
  • if R,B>T=M
• For 2
  • if 1 were to play T,L>R>C
  • if M,C>R>L
  • if B,R>L=C
• Thus,there is no strictly D strategies..
• Next,we think best response to the each strategies,
• for 1
  • if 2 were to play L,M is the best.
  • if C,T.
  • if R,B.
• For 2
  • if 1 were to play T,L is the best.
  • if M,C.
  • if B,R.
• In that process, we can see (B,R) as a only strategy pair that satisfies (NE).

参考

Robert Gibbons [1992]：『Game　Theory　for　applied　economists』