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You can sell the goods separately, in a pure bundle or in a mixed bundle. (If
indifferent between two options, assume consumers choose the alternative which
maximizes the firm's profit).
• Which strategy would maximize the profit of the firm? (A detailed answer is
expected, show the steps of your reasoning).
Exercise 3
Consider the following game:
a
b
с
A 0,11.5 0,0 10,10
B 0,0
6,6
0,0
C 4,4 0.0 11.5, 0
1. Find all the Nash equilibria of the stage game. Express the resulting payoffs.
Suppose the game is played twice and the discount factor is d = 1. Players
observe the actions chosen in the first play of the game prior to the second
play.
2. Can you propose a Subgame Perfect Nash Equilibrium where players get 10 in
the first period? Show that it is an equilibrium.
Suppose the game is played twice and the discount factor is d = 1/2.
3. Can you propose a Subgame Perfect Nash Equilibrium where players get 10 in
the first period?
Exercise 1
Use successive elimination of dominated strategies to solve the following game.
Explain the steps you followed.
Left Middle Right
(4,3) (2,7) (0,4)
Down (5,0) (5, -1) (-4,-2)
Up
Exercise 2
Consider the following game:
Left Middle Right
Top (4,2) (?,2) (3,1)
Middle (3,5) (2,?) (2,3)
Bottom (2,3) (3,4) (4,2)
1. Complete the payoffs of the game table above so that Player 2 (column player)
has a dominant strategy. State which strategy is dominant. (Note: there are
many equally correct answers.)
2. Complete the payoffs of the game table above so that neither player has
a dominant strategy, but also so that each player does have a dominated
strategy. State which strategies are dominated and state by which strategy it
is dominated. (Again, there are many equally correct answers.)
1
Exercise 3: Air Strike
Army A has a single plane with which it can strike one of two possible targets.
Army B has one anti-aircraft gun that can be assigned to one of the targets. The
value of target 1 is 1 and the value of target 2 is 2. Army A can destroy a target
only if the target is undefended and A attacks it. Army A wishes to maximize the
expected value of the damage and army B wishes to minimize it. If Army A attacks
a defended target, both payoffs are 0. Players move simultaneously.
1. Express the normal form of the game (Payoff table)
2. Find the Nash equilibrium.