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 answer5. Is collusion possible in this game? Explain your answer.
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.
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.
Considering 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 considering 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 adapt to sink wide well as it gives companies the optimal pay-off/profit independent of the rival's strategy.
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