Question

DEVTRACO has purchased a 2-year lease on land adjacent to the land leased by

Johnson. The land leased by DEVTRACO lies above the same crude oil deposit. Assume each company sinks wells of the same size at the same time. If both companies sink wide wells, each will extract 2 million barrels in 6 months, but each company will receive profit of only $1 million. On the other if each company sinks a narrow well, it will take a year for Johnson and DEVTRACO to extract their respective shares, but their profits will be $14 million apiece. Finally, if one company drills a wide well while the other company drills a narrow well, the first company will extract 3 million barrels and the second company will extract only 1 million barrels. In this case, the first company will earn profits of $16 million and the second company will actually lose $1million.

1. Illustrate this using a normal form game.

2. Does either firm have a strictly dominant strategy? If yes, what is (are) these

strategies? Explain your answer.

3. What strategy will each firm adopt? Explain your answer.

4. Does this game have a Nash equilibrium? Explain your answer

5. Is collusion possible in this game? Explain your answer.

Answer 1

Answer 1   

Johnson

Wide Narrow

DEVTRACO   Wide    1,1 16,-1

Narrow -1,16 14,14

Answer 2

Yes, both the firms have strictly dominant strategies. The dominant strategy for Devtraco is to dig wide wells. And the dominant strategy forJohnson is also to dig wide wells. This is because either firm that digs wide wells gets either $1 million or $16 million, which are higher than $-1 million or $14 million respectively, depending upon other company's strategy.

Answer 3

Each firm will adopt the strategy of building wide wells. This is because the wide wells will give profits of either $1 or $16 depending on what the other competitor does. However, there will not be any loss to any of the firms if they choose to dig wide wells. Thus, they will always choose this strategy.

Answer 4

Yes, this game has a Nash Equilibrium.

The Nash Equilibrium of the game is: (Wide, Wide) = (1,1)

Answer 5

Since this is a one time game and not repeated games, collusion may not be possible. This is because of the fear that the other company may sink a wide well (cheat after colluding) and thus, the other firm would lose out $1.