Alice, Bill and their mother are still deciding how to split a chocolate bar. Assume that the chocolate bar has 8 squares, so can only be divided into multiples of 1/8. Assume also that each only wants to maximise how much chocolate he or she gets.

Consider the following sequential move game in the first stage, the mom divides the chocolate bar into 3 pieces. In the second stage, Alice takes one of these three pieces. In the second stage, Bill takes one of the remaining two pieces. The mom then gets the piece that remains. This game has two SPNE. In both of them, the mom gets the same fraction of the chocolate. What is this fraction? Explain in two sentences, and feel free to include a drawing if it helps.

The 2 SPNE of this game where Mom gets the same fraction of chocolate are

(I) x1 =3/8, x2 =3/8, x3 = 2/8

(II) x1 =4/8, x2 = 2/8, x3 = 2/8

But why these 2? please explain thanks !