Question

1. Mexico and the members of OPEC produce crude oil. Realizing that it would be in their best interests to form an agreement on production goals, a meeting is arranged and an informal, verbal agreement is reached. If both Mexico and OPEC stick to the agreement OPEC will earn profits of $200 million and Mexico will earn profits of $100 million. If both Mexico and OPEC cheat then OPEC will earn $175 million and Mexico will earn $80 million. If only OPEC cheats, then OPEC earns $185 million and Mexico $60 million. If only Mexico cheats, then Mexico earns $110 million and OPEC $150million.
   
   
   OPEC Cheat Abide Cheat Mexico Abide
   

1. Fill in the chart.
2. Does Mexico have a dominant strategy? If so, what is it?
3. Does OPEC have a dominant strategy? If so, what is it?
4. Is there a Nash equilibrium? If so, what is it?
5. Is this game an example of a prisoner’s dilemma? Why or why not?

Answer 1

(a)

It has been stated that if both Mexico and OPEC stick to the agreement OPEC will earn profits of $200 million and Mexico will earn profits of $100 million. If both Mexico and OPEC cheat then OPEC will earn $175 million and Mexico will earn $80 million. If only OPEC cheats, then OPEC earns $185 million and Mexico $60 million. If only Mexico cheats, then Mexico earns $110 million and OPEC $150million.

Following is the complete chart -

OPEC Cheat Abide Cheat $80 million, $175 million $110 million, $150 million Mexico Abide $60 million, $185 million $100 million, $200 million

(b)

If OPEC cheats then Mexico can earn $80 million if it cheats and $60 million if it abides. Profit is higher in case the Mexico cheats. So, Mexico will cheat if OPEC cheats.

If OPEC abides then Mexico can earn $110 million if it cheats and $100 million if it abides. Profit is higher in case the Mexico abides. So, Mexico will cheat if OPEC abides.

It can be seen that Mexico will cheat whatever be the strategy of OPEC.

So,

Mexico have a dominant strategy. The strategy is to cheat.

(c)

If Mexico cheats then OPEC can earn $175 million if it cheats and $150 million if it abides. Profit is higher in case the OPEC cheats. So, OPEC will cheat if Mexico cheats.

If Mexico abides then OPEC can earn $185 million if it cheats and $200 million if it abides. Profit is higher in case the OPEC abides. So, OPEC will cheat if Mexico abides.

It can be seen that OPEC's strategy changes as the strategy of Mexico changes.

So,

OPEC does not have a dominant strategy.

(d)

Mexico has dominant strategy. Its dominant strategy is to cheat.

When Mexico cheats, OPEC also cheats.

So,

This game has a Nash equilibrium.

The Nash equilibrium is that both Mexico and OPEC will cheat.

The Nash equilibrium is (Cheat, Cheat).

(e)

A game is an example of Prisoners dilemma if cooperation gives higher combined payoff to both players but players choose non-cooperative outcome.

In the given case, if both Mexico and OPEC abide by the agreement then their profits would be higher than when they both cheat on the agreement.

However, they are choosing to cheat.

So,

This game is an example of Prisoner's dilemma.