Two-person fair division of indivisible objects
Image taken from http://www.divorceny.com Fair allocation of objects is one of the most pressing issues faced by society. “Fairness” is a prickly topic with people coming up with different notions of what fairness should mean . One of the most established notions of fairness is envy-freeness which requires that no agent should prefer another agent’s allocation. EF (Envy-freeness) by itself does not guarantee desirable allocations. For example, an allocation which leaves agents empty-handed is envy-free as well! Thus, we would like to allocate all the objects to the agents i.e., the assignment should be complete. Unfortunately, there may not exist a complete and envy-free assignment. This can illustrated by consider the setting in which there is exactly one object. Then, any agent who does not get the object will be envious of the agent who gets the object. In view of this predicament, in a recent issue of Notices of the AMS , Brams, Kilgour and Klamler (2014...