Problem: Suppose that a cake is being divided in the following way among two players. Each player writes down a number from zero to one on his piece of paper. Then both players turn over their pieces of paper. If the sum is less than or equal to one, each player gets a share of the cake equal to the number he wrote. If the sum is bigger than one, each player gets nothing.
What are the pure strategy Nash Equilibria of this game? Do they help you at all in predicting the result of the game?