Question

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

Clampett. The land leased by TEXplor 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 GHC 1 million. On the other if each company sinks a narrow well, it will take a year for Clampett and TEXplor to extract their respective shares, but their profits will be GHC14 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 GHC 16 million and the second company will actually lose GHC 1million.

1. Illustratethisusinganormalformgame. (5marks)

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. DoesthisgamehaveaNashequilibrium?Explainyouranswer

5. Iscollusionpossibleinthisgame?Explainyouranswer.

Answer 1

1. The game can be illustrated using a normal form with the following pay-off matrix. There are two sets of actions {Sink wide well, Sink narrow well} and there are two players {Company 1, Company 2}. The pay-offs (cells) represent the profit/loss from each of the 2 sets of strategies adopted by each of the two companies.

		Company 2
		Sink wide wells	Sink narrow wells
Company 1	Sink wide wells	(1,1)	(16,-1)
Sink narrow wells	(-1,16)	(14,14)

2. Yes, each of the firms has a strictly dominant strategy. Sinking wide wells is the strictly dominant strategy of each firm. The reason is that irrespective of the strategies adopted by the other player, it is optimal for the respective player to sink wide well (as the pay-offs are maximum when sinking wide well as opposed to sinking narrow well).

3. Given the existence of a strictly dominant strategy, each firm will sink wide well.

4. Yes, there exists a Nash equilibrium which is represented by the underlined pay-offs (in both of the firm's strategies) in the above matrix. The Nash equilibrium is to sink wide wells for each firm as then there is no tendency for each of them to move away to other strategy, pay-off (1,1).