Fair division problems | Department of Mathematics

Fair division problems

Event Information
Event Location: 
GAB 105, 4-5 PM; Refreshments: GAB 472, 3:30 PM
Event Date: 
Tuesday, October 15, 2013 - 4:00pm

The general subject of this talk will be the question of whether an object (such as a cake or piece of land) can be divided among N people so that each person receives a fair portion, according to his own values. Formally, there are N normalized (i.e., total mass 1) measures on the same object - a measurable space - and a typical goal is to find a partition of the object into N (measurable) pieces, and allocate one piece to each participant, in such a way that each values his own piece at least 1/N, or as large as possible. Classical results include Steinhaus's "Ham Sandwich Problem", Dubins and Spanier's "Sliding Knife Algorithm", and Fisher's "Problem of the Nile". Several recent results will be discussed, including basic counterexamples in fair-division theory and a stronger form of the Ham Sandwich Theorem. Generalizations based on Lyapounov's Convexity Theorem will be also be mentioned, along with several applications and open problems. The talk will be aimed for the non-specialist.

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