Chapter 2: separate solutions

Question 1

Verify the decomposition.

The joint gain is 0.80-0.20=0.60 and the isolated gains are 0.30-0.20=0.10 and 0.25-0.20=0.05. The interaction is 0.80-0.30-0.25+0.20=0.45, and 0.60=0.10+0.05+0.45.

Question 2

What changes when only the intact budget doubles?

The changed budgets are 10, 10, 10 and 20, so the matched-budget flag becomes false. The scores are unchanged, so the numeric contrast remains 0.45.

Question 3

Is -0.30 a cooperation fraction in the transfer case?

No. In the transfer case the interaction is 0.70-0.55-0.50+0.20=-0.15 and the joint gain is 0.70-0.20=0.50, so the signed ratio is -0.15/0.50=-0.30. That value lies outside the chapter's fraction domain [0,1].