Least manipulable Envy-free rules in economies with indivisibilities

We consider envy-free and budget-balanced allocation rules for problems where a number of indivisible objects and a fixed amount of money is allocated among a group of agents. In finite economies, we identify under classical preferences each agent's maximal gain from manipulation. Using this result we find the envy-free and budget-balanced allocation rules which are least manipulable for each preference profile in terms of any agent's maximal gain. If preferences are quasi-linear, then we can find an envy-free and budget-balanced allocation rule such that for any problem, the maximal utility gain from manipulation is equalized among all agents.