The Egalitarian Equivalent and Gain Max-Min Solutions for Package Assignment Problems
School of Petroleum Management, PDPU
March 13, 2012
This paper proves the existence of egalitarian equivalent and gain max-min solutions for package assignment problems and shows that they satisfy the “fair share guaranteed” property. It is also shown that if the preferences of the agents satisfy “diminishing marginal willingness to pay” then the gain max-min solution satisfies resource monotonicity and the egalitarian equivalent solution satisfies resource monotonicity only if there are two agents. For more than two agents, the egalitarian equivalent solution does not in general satisfy resource monotonicity even if preferences of all agents satisfy “diminishing marginal willingness to pay”. Further, the egalitarian equivalent solution satisfies population monotonicity but the gain max-min solution does not. However it is not the case that if we apply the egalitarian equivalent solution then for all package assignment problems all the original agents are better off after the arrival of a new agent; nor is it the case that if we apply the egalitarian equivalent solution then for all package assignment problems all the original agents are worse off after the arrival of a new agent.
Number of Pages in PDF File: 17
Keywords: package assignment, fair allocation, egalitarian equivalence, gain max-min, resource monotinicity
JEL Classification: D63, D79
Date posted: March 20, 2012 ; Last revised: August 23, 2012