Question

Question Two                                                                                    
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

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 represented in each of the cells of the matrix for each firm with their as well as their counterpart's strategy.

		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, both of the firms have a strictly dominant strategy. The strictly dominant strategy for both of the players is to Sink wide well. The reason is that irrespective of their opponent's strategy, it is optimal (max pay-off) for the player to Sink wide well.

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

4. Yes, 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 deflect to any other strategy.