Consider two companies with mining rights to the same region. They could mine in an environmentally friendly manner or aggressively. If both mine environmentally friendly, profits are 100 million for each in a given year.
If they both mine aggressively, the government will step in and fine them, meaning that they will make 75 million each. Finally, the government will not step in if only one of the companies mines aggressively, meaning that the aggressive miner will make 120 million while the environmentally friendly miner will lose out in capacity and make 50 million.
a) Write the normal form of the game and point out the Nash equilibrium if the game is played only once. (2)
b) What will be the rollback equilibrium if the two companies mine the same region three years in a row? (2)
c) Now assume that the game is repeated infinitely. What rate of the return value will sustain the environmentally friendly strategy as the Nash equilibrium if one of the companies is playing a grim strategy? (3)
d) Now assume that the game is repeated infinitely. What rate of the return value will sustain the environmentally friendly strategy as the Nash equilibrium if one of the companies is playing a tit-for-tat strategy?
(3)
e) Assume now that one of the companies wants to sign a contract that states that the other company will mine environmentally friendly while it will mine aggressively for perpetuity. What would be the price for the right to mine aggressively if the expected rate of return on money is 10%?