Question

3. A New York Times article (5/9/88) reported that according to the International Energy Agency "oil production by OPEC rose to 18.2 million barrels/day in April from 17.7 m. barrels in March." Part of this increase was attributed to Iraq's refusal to sign the group's production sharing program and its subsequent increase in output to 2.6 m. barrels/day. OPEC's other 12 members however cooperated with their agreements and produced close to their agreed upon quota. Suppose we could model this issue as a game between Iraq and the rest of OPEC. Each player has two strategies: Low quantities of oil production and High quantities of oil production. The extensive form (a.k.a. tree form) of the game is as follows: (40,10) Note that the profits are written as (Rest of OPEC's profit, Iraq's profit). Profit in $billions. a) What is the Subgame Perfect Nash Equilibrium of this game? b) Suppose that Iraq and the rest of OPEC cannot observe each other's actions, i.e. they were to play this game simultaneously. Write down the normal form representation of this game. c) Do any of the players have a "dominant strategy?" If so, what is it? d) If you were to advise the OPEC ministers, could you suggest an outcome that is better for the group than the outcome you found above? Explain? What terms would you suggest be written into any contract the two parties endorse.

Answer 1

solution: (3) Given game tree is, Rest of op ec low Cirag) High Gragr) Ctugšio) (139,8is) ($20, 83 (812285) @ Subgame perfect Nagh Equilibrium of this game is: for subgame perfect wash expilibrium , we have to first find out the pay offs of Iraq then given this choice what will rest of the opec choose in the left side., Drag will always choose tigh as he gets a higher pay off ($157 810) on the right hand side, Drag will choose High I as he gets a higher pay off ($5>83)

• Af Iraq chooses high in both cases, the rest of the opec will choose low, as it gives a higher payoff C$ 30 >813): sub perfect Nash equilibrium = (low High) = ($30, $15) ① Normal, form representation of the game is: Iraq low High low High 40,0 30,15 20,3 . 12,5 Rest of opec © which player have dominant strategy and they are: >> Both players have a dominant strategy. for rest of opec, Strategy low dominates strategy high

for Iraq, strategy high dominaty strategy low. d) Suggestion: • Rest of OPEC can geta higher pay off if they choose Strategy. Low given that Iroq chooses Strategy low . But it would deerease the pay off of Iraq, and it would not be an efficient outcome for both the parties _ o