Question #97869

a) Consider the following payoff matrix of player 1 and player 2

Production Launching Game

PLAYER 2

PRODUCT A

PRODUCT B

PRODUCT C

PRODUCT D

3, 6

7,1

10,4

PLAYER 1

PRODUCT E

5,1

8,2

14,7

PRODUCT F

6,0

6,2

8,5

Using iterative elimination of dominated strategies approach, we can find the equilibrium of the game

(6Marks).

b) Given the following production function;

Required:

Calculate the degree of homogeneity of the above function and comment

on the returns to scale.

Production Launching Game

PLAYER 2

PRODUCT A

PRODUCT B

PRODUCT C

PRODUCT D

3, 6

7,1

10,4

PLAYER 1

PRODUCT E

5,1

8,2

14,7

PRODUCT F

6,0

6,2

8,5

Using iterative elimination of dominated strategies approach, we can find the equilibrium of the game

(6Marks).

b) Given the following production function;

Required:

Calculate the degree of homogeneity of the above function and comment

on the returns to scale.

Expert's answer

Start with player one:

If player two chooses product A, player one should choose product B (7,1 versus 3,6).

If player two chooses product C, player one should also choose product C (10,4 versus 14,7).

Therefore, the optimal strategy is to always choose product C (for both players), this means that (product C, product C) is the only iterative elimination.

If this game is played multiple times, then we start at the end (the third playing of the game). At the last stage, this is like a one shot game (there is no future). Therefore, on the last day, the dominant strategy is for both players to choose Product C.

There is no data given about the production function to calculate its degree of homogeneity.

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