Game Theory&Economic Behavior
Name: ___________________________
1
Score: ________/ 20 Game Theory – ECN 416
FOSTER
Assignment #4: Sequential Games and Subgame Perfection
Use a pencil. Put your answer in the appropriate place and box it. Show any work necessary to ensure
partial credit. Staple these pages.
1) Diagram the game below in extensive form, then solve using backwards induction. (10 points)
a. PLAYER ONE chooses LEFT, CENTER, OR RIGHT.
b. PLAYER TWO chooses UP, MIDDLE, OR DOWN.
c. PLATER ONE chooses RED, GREEN, OR BLUE.
Payoffs are:
LUR (2 , 3) CUR (9 , 1) RUR (1 , 1)
LUG (1 , 7) CUG (8 , 6) RUG (2 , 2)
LUB (5 , 4) CUB (4 , 5) RUB (3 , 3)
LDR (3 , 9) CDR (0 , 2) RDR (4 , 4)
LDG (9 , 1) CDG (7 , 8) RDG (5 , 5)
LDB (8 , 6) CDB (5 , 4) RDB (6 , 6)
LMR (4 , 5) CMR (3 , 9) RMR (7 , 7)
LMG (0 , 2) CMG (2 , 3) RMG (8 , 8)
LMB (7 , 8) CMB (1 , 7) RMB (9 , 9)
Name: ___________________________
2
Name: ___________________________
3
2) Suppose that a firm is considering entry into a new market. The market contains one firm
already. The strategies for ENTRANT are ENTER or DO NOT ENTER. The strategies for
INCUMBENT are FIGHT or DO NOT FIGHT. Payoffs are listed below as (ENTRANT, INCUMBENT).
INCUMBENT
FIGHT
DO NOT
FIGHT
E N
T R
A N
T
E N
T E
R
(-5 , -5) (2 , 2)
D O
N O
T
E N
T E
R
(0 , 5) (0 , 5)
a) What are the Pure Strategy Nash Equilibria (PNE) of this game? (2 points)
b) Diagram this game as a sequential game with perfect information where ENTRANT acts first.
Solve the game and state whether the solution is Subgame Perfect. (4 points)
c) Diagram this game as a sequential game with perfect information where INCUMBENT acts first.
Solve the game and state whether the solution is Subgame Perfect. (4 points)