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. 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. (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. Does this game have a Nash equilibrium?Explainyouranswer

5. Is collusion possible in this game?Explainyouranswer.

Answer 1

Given that lease on land Tex plos has purchased a's . year adjacent to the land leased by clampett The normal form of the game can be. Enestated below: ITExplor wide well TEx plor narrow well Clampett wide well CIM, IM) (-IM, I6M) Clamper nago will (16M,-IM) Cibern, IHM) Cell well In the normal form above, each die presents the payoffs I profits that can be earned by each firm. the consist of the choice of si estrategies in this game sinking wide well or a narrow consider Tex plor first, it etampert Chooses to sink a wide well, TEX PLOY coชก. a higher pay off by goinking a wide well (I-1). qsimilarly, If clampett chooses to sink a narco wen), TER ploo errons a higher pay off by sinking a wide well. Thus, PIO irrespective of what clampert chooses to do, Tex psinics a wide well mating it it's dominant Strategy Next consider clampett, the same ar Fonoluring above, Clampett argument coide well isrespective of also Alurays chooses to pink a What Texplor does. Thus, Poinking a wide dominate strategy: ܠܘ coen

3) Both forms will adopt the Staategy of Binicing on coide well, reince it gields higher payoff irrespective of the estrategy a dopled by the other tiram Yes, This game has a has a Nash equilibrium where both fioms fo now their dominant Strategies

Thus, ( wide well, wide coll) is the Nash equilibrium of this game, yielding a pay off of Grc1 million for each of the firms is consion is persible in this game since it will bring larger payoff to both the firms. If both the firmas larger than the easilni brim pay of GHC I minion. 97 - there's high probability of festere interactin Thos, between the teen firms, Colosion can be sustained. Thank you