How a game can be represented?
Normal vs Extension Form
Commonly for dynamic games (involves sequential move)
Credibility
Perfect information: at each node of the game tree, the player
whose turn to move knows which node she is at and how she
got there
Pure strategy
Backward-induction outcome
Example
Node 1: Node 2: Node 3: Player 1’s pay off Player 2’s pay off
Player 1’s Player 2’s Player 1’s
first move first move second move
Strategies of Strategies of Strategies of
Player 1’s Player 2’s Player 1’s
first-move first-move second-move
Strategies of Strategies of
Player 1’s Player 1’s
first-move second-move
Backward Induction Solution
Start from the end
Last node is player 1 move, see pay off of player 1.
“d” higher pay off
Summarize
Last node become player 2 move, see pay off of
player 2.
(3,1) “r” higher pay off
Summarize
Last node become player 1 move, see pay off of
player 1.
“D” higher pay off
(0,2)
BI={[D,d],r} with pay off {1,0}
Transformation to Normal Form
Player 2
Player 1
From extensive form
to the normal form
P2 i r Nash Equilibrium
P1
Uu 2,4 0,2 P2 i
Ud 3,1 0,2 P1
Du 1,0 1,0 Uu 2,4
Dd 1,0 1,0 Ud 3,1
Du 1,0
Dd 1,0
P2 r
P1
Uu 0,2
Ud 0,2
Du 1,0
Dd 1,0
P2 i r Nash Equilibrium (NE)
P1
P2 i r
Uu 2,4 0,2
Ud 3,1 0,2 P1
Du 1,0 1,0 Uu 2,4 0,2
Dd 1,0 1,0
P2 i r
P1
Ud 3,1 0,2
P2 i r
P1
Du 1,0 1,0
P2 i r
P1
Dd 1,0 1,0
P2 i r
P1
Uu 2,4 0,2
Ud 3,1 0,2
Du 1,0 1,0
Dd 1,0 1,0
