Currency Crisis Model

Each investor has one million pounds and is choosing to invest in pounds or in marks. The government has B pounds worth of marks in its foreign reserves that it is willing to use to defend a fixed exchange rate. There are a total of 2000 investors.

1. Imagine you were an individual investor, and could observe the government's stockpile B and every other investor's actions. Suppose B is one billion pounds (for only this question). Call D the number of other investors that invest in marks. Describe your best response as a function of D. What are the possible Nash equilibria?

2. Suppose that you couldn't observe the other investor's actions, but you did know their strategies. 500 of the other investors invest in marks if B is less than a billion. The other 1500 invest in marks if B is less than 500 million.

What is your best response to these strategies, as a function of B?

3. In the last question, was every investor playing a best response? Who was not?

4. Now suppose no one sees the true B. Instead everyone sees Bi , which is distributed uniformly between B 1 and B + 1.

Assume everyone else adopts the cutoff strategy that if the Bi they see is less than 500 million pounds, they will invest in marks, and if their Bi is above 500 million pounds, they will invest in pounds.

What should you do if you get a signal of Bi = 6 million pounds? What if Bi = 4, 999, 998 pounds?

5. If B was exactly 500 million pounds, how many investors would invest in marks? What would happen to the exchange rate?

6. What should you do if Bi = 4, 999, 999.999 pounds? Hint: figure out approximately how many other investors you think are going to invest in marks. Compare that to approximately your best guess of the reserves the government has. What is going to happen to the exchange rate?

What does your answer imply about the cutoff strategy that everyone else is using? Is it their best response?

7. What cutoff strategy is a Nash equilibrium?