Consider the following game: Both Alice and Beatrice simultaneously and independently choose a real number that is higher than 0 (any positive real number is okay). Then a bank pays each of them an amount of money (in Canadian dollars) that is equal to the multiplication of the numbers Alice and Beatrice picked. For example, if Alice picks 10 and Beatrice picks 20, then each receives 20 x 10 = $200.

Suppose that the Bank has no shortage of money, and both Beatrice and Alice prefer more money to less.

This game has no Nash equilibrium in pure strategies.

A TRUE

B FALSE