Firm B Use Double Coupons Stay Open 24 Hours Firm A Use Double Coupons 40, 60 55
ID: 1254342 • Letter: F
Question
Firm B
Use Double Coupons
Stay Open 24 Hours
Firm A
Use Double Coupons
40, 60
55, 45
Stay Open 24 Hours
45, 55
60, 40
a) Does either firm have a dominant strategy? If so, what is it?
b) Solve for the Nash equilibrium of the game.
Player 2
Left
Right
Player 1
Up
X, 7
4, 6
Down
5, 8
9, Y
a) What necessary requirements do the unknown payoffs (X or/and Y) have to satisfy so that (Up, Left) is a Nash equilibrium?
b) What necessary requirements do the unknown payoffs (X or/and Y) have to satisfy so that (Up, Left) is the unique Nash equilibrium?
a) Create a game tree (or extensive form) of this game that represents the situation described.
b) Solve for the (Subgame Perfect) equilibrium of the game.
Firm B
Use Double Coupons
Stay Open 24 Hours
Firm A
Use Double Coupons
40, 60
55, 45
Stay Open 24 Hours
45, 55
60, 40
Explanation / Answer
Firm B
Use Double Coupons
Stay Open 24 Hours
Firm A
Use Double Coupons
40, 60
55, 45
Stay Open 24 Hours
45, 55
60, 40
a) Does either firm have a dominant strategy? If so, what is it?
Yes, Firm A has a dominant startegy to stay open while Firm B Uses double coupons
b) Solve for the Nash equilibrium of the game.
The nsh equilibrium is for Firm A to stay open and Firm B to use double coupons
Player 2
Left
Right
Player 1
Up
X, 7
4, 6
Down
5, 8
9, Y
a) What necessary requirements do the unknown payoffs (X or/and Y) have to satisfy so that (Up, Left) is a Nash equilibrium?
In this case, X must be greater than 5 to be a nash equilibrium
b) What necessary requirements do the unknown payoffs (X or/and Y) have to satisfy so that (Up, Left) is the unique Nash equilibrium?
In this case, x must be greater than 5 and y must be less than 8
a) Create a game tree (or extensive form) of this game that represents the situation described.
2. pepsi develope-------(600,600)
1. coke develop-----------
2. pepsi dont develop-------(800,200)
new product--- 2. pepsi develop---------(200,800)
1.coke dont develop
2. pepsi dont develop------(400,400)
b) Solve for the (Subgame Perfect) equilibrium of the game
to solve this we use backward induction. Since pepsi is player 2 we compare his choice first then decide what coke will do. I will highlight.
SPNE is both to produce new product. I hope this tree is clear. It starts with the decision of coke to develop of not. Then pepsi develop or not based on cokes decision. Let me know if you haave any questions. For the backward inductiong pepsi compares payoff of two choices if coke develops then 2 choices if coke doesnt. Then coke choses payoff based on those 2 choices.
Firm B
Use Double Coupons
Stay Open 24 Hours
Firm A
Use Double Coupons
40, 60
55, 45
Stay Open 24 Hours
45, 55
60, 40
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