A fair arrangement is one in which each sibling feels he or she is getting at least of the value of the object. An equitable arrangement is one in which each sibling feels he or she is getting the same fraction of the value. An envy-free arrangement is one in which no sibling thinks some other sibling is getting more value than he or she is.

Start by specifying each sibling's bid (aka valuation/utility) for the jointly owned object. You then specify who is to get the object and see what, if any, are the possible fair, equitable, and envy-free arrangements.