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.

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.

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. 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):- This can be illustrated in a game-theoretic environment in a normal form game with the following pay-off matrix. There are 2 players in this game, {Company 1, Company 2} and the strategy set is {Sink wide well, Sink narrow well}. The pay-offs are spoken to in each of the cells of the matrix for each firm with their as well as their counterpart's strategy.

	Clampett wide well	Clampett narrow well
TEXplor wide well	(1M, 1M)	(16M, -1M)
TEXplor narrow well	(-1M, 16M)	(14M, 14M)

2):- Consider TEXplor first. On the off chance that Clampett decides to sink a wide well, TEXplor earns a higher payoff by sinking a wide well ( 1> - 1). Similarly, if Clampett decides to sink a narrow well, TEXplor earns a higher payoff by sinking a wide well. In this manner, independent of what Clampett decides to do, TEXplor sinks a wide well, making it its dominant strategy.

Next consider Clampett. Following the same argument as above, Clampett also always decides to sink a wide well, regardless of what TEXplor does. Hence, sinking a wide well is its dominant strategy.

3):- Each firm will adopt to sink wide well as it gives them the optimal pay-off/profit independent of the rival's strategy.

4):- Truly, there exists a Nash equilibrium which is for both to Sink wide well and earn a pay-off of 1 million each (1,1). There is no tendency here for each one to redirect to any other strategy.

5):- Collusion is conceivable in this game since it will bring a larger payoff to both the organizations. On the off chance that both the organizations decide to plot and sink narrow wells, both will get a payoff of GHC 14 Million, which is a lot larger than the equilibrium payoff of GHC 1 Million. Subsequently, if there's a high probability of future interaction between the two firms, collusion can be sustained.

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