Fair Allocation with Money: What is Your Objective?

When allocating indivisible items, there are various ways to use monetary transfers for eliminating envy. Particularly, one can apply a balanced vector of transfer payments, or charge each agent a positive amount, or – contrarily – give each agent a positive amount as a ``subsidy’'. In each model, one can aim to minimize the amount of payments used; this aim translates into different optimization objectives in each setting. This note compares the various models, and the relations between upper and lower bounds for these objectives.