4. In 1970 economist Martin Shubik proposed the following game that involved auctioning off a one-dollar bill with the following rules:

1. The highest bidder wins the dollar bill and pays his bid.

2. The second-highest bidder also has to pay the amount of his last bid—and gets nothing in return.

3. Each new bid has to be higher than the current high bid.

4. The game ends when there is no new bid within a specified time limit.

a. When the dollar was auctioned off, do you suppose that the highest bid was less than or greater than a dollar?

Why?

b. Can a rational player ever lose the auction once he has started bidding?

c. Is it rational to begin bidding?