Two players, 1 and 2, simultaneously and independently choose numbers between 1 and 15. If both choose the same number x; each gets x.

If one chooses a lower number than the other, she gets her number +5 and the one with the higher number gets his number -5.

Thus if one chooses 6 and the other 10, the one choosing 6 gets 11 and the one choosing 10 gets 5.

(a) Is there an equilibrium in which both choose 15?

(b) Is there an equilibrium in which either player chooses 1?

(c) Show that there is a mixed strategy equilibrium in which each player accords probability 1/10 to each number between 6 and 15.