Ten (10) people have the opportunity to buy tickets for a lottery that offers a

prize of $30. The price of a ticket is $1. Each person has just $2 with which

to buy tickets. The people simultaneously buy their tickets. Then they write

their names on the tickets they bought, and deposit the tickets in a hopper.

The winner of the prize is determined by a random draw of one ticket from

the hopper. If no tickets are bought the prize is awarded to no one. All 10

people are risk neutral.

Is the following statement TRUE / FALSE? Explain your answer.

(There is a Nash equilibrium in which all 10 people each buy the same number

of tickets)