Consider two companies with mining rights to the same region. They could mine in an environmentally friendly manner or agressively. If both mine environmentally friendly, profits are 100 million for each in a given year. If they both mine agressively, 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 agressively, meaning that the aggresive miner will make 120 million while the environmentally friendly miner will loose 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 ina row? (2) c) Now assume that the game is repeated infinitely. What rate of return value that will sustain the environmentally friendly strategy as the Nash equilibrium if one of the companies is playing a grim strategy? (3
Consider two companies with mining rights to the same region. They could
mine in an environmentally friendly manner or agressively. If both mine
environmentally friendly, profits are 100 million for each in a given year.
If they both mine agressively, 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 agressively, meaning that the
aggresive miner will make 120 million while the environmentally friendly
miner will loose 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 ina row? (2)
c) Now assume that the game is repeated infinitely. What rate of return
value that 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 return
value that will sustain the environmentally friendly strategy as the Nash
equilibrium if one of the companies is playing a tit for tat strategy 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 agressively for perpeuity. What would be the price for the right
to mine agressively if the expected rate of return on money is 10%? (2)
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