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. 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. The normal form of the game can be illustrated below:

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

In the normal form above, each cell represents the payoffs/profits that can be earned by each firm. The strategies in this game consist of the choice of sinking a wide well or a narrow well.

Answer 2. Consider TEXplor first. If Clampett chooses to sink a wide well, TEXplor earns a higher payoff by sinking a wide well ( 1> -1). Similarly, if Clampett chooses to sink a narrow well, TEXplor earns a higher payoff by sinking a wide well. Thus, irrespective of what Clampett chooses to do, TEXplor sinks a wide well, making it its dominant strategy.

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

Answer 3. Both firms will adopt the strategy of sinking a wide well, since it yields a higher payoff irrespective of the strategy adopted by the other firm.

Answer 4. Yes, this game has a Nash equilibrium where both firms follow their dominant strategies, Thus, (wide well, wide well) is the Nash equilibrium of this game, yielding a payoff of GHC 1 Million for each of the firms.

Answer 5. Collusion is possible in this game since it will bring a larger payoff to both the firms. If both the firms choose to collude and sink narrow wells, both will get a payoff of GHC 14 Million, which is much larger than the equilibrium payoff of GHC 1 Million. Thus, if there's a high probability of future interaction between the two firms, collusion can be sustained.