Question

The oil ministers of Brazil and Iran have agreed to restrict their output in order to raise prices and increase profits. The countries have to choices: to stick to their collusive agreement or to cheat. Their payoff matrix is in billions of dollars is as follows:

	Iran
Brazil		Collude	Cheat
	Collude	10,10	5,15
	Collude	15,5	7,7

(a) What is a dominant strategy? Does Saudi Arabia have a dominant strategy in this game? Explain your answer.

(b) Which outcome maximizes joint profits in this game? Which outcome do you predict will emerge assuming these countries only interact with each other once? Explain your reasoning.

(c) Would your answer to part (b) above change if the countries interacted with each other repeatedly? Explain why.

Answer 1

Answer

Part a)

In game theory, a dominant strategy is the course of action that results in the highest payoff for a player regardless of what the other player does.

Yes, both the countries in this game have their own dominant strategies. This is because:

Case 1: When Brazil Cheats, its payoffs are $15 and $7, which are greater than $10 and $5 respectively. (as per the cases whereby Iran colluded or cheated respectively).

Case 2: When Iran Cheats, its payoffs are $15 and $7, which are greater than $10 and $5 respectively. (as per the cases whereby Brazil colluded or cheated respectively).

Part b)

The outcome where both the countries collude maximises the joint profits. The profits would be $10 billion for each country. However, the income of $7 billion will emerge assuming for both these countries if they interact only once with each other. This is because no country would trust each other and would fear that they would lose out on their profits if the other country cheated on them and they tried to collude. Thus, because of this fear, they would not collude and thus, cheat on each other.

Part c)

If the countries interacted with each other repeatedly, the countries would collude with each other and the payoffs would increase to $10 biilion each. This is because it will build a trust for each other and they both will follow a tit-for-tat strategy. Thus, both would continue to collude and earn higher profits.