Two people have $10 to divide between themselves. They use the following procedure to divide the money. Each person names a nonnegative integer between 0 and 10. If the sum of the amounts that the people name is at most 10 then each person receives the amount of money he names (and the remainder is destroyed). If the sum of the amounts the people name exceeds 10 and the amounts named are different, then the person who names the smaller amount receives that amount and the other person receives the remaining money. If the sum of the amounts the people name exceeds 10 and the amounts named are the same then each person receives $5.

(a) Formulate this situation as a strategic game

(b) Find all pure Nash equilibria.