Title

Cutting Cakes with Linked Preferences

Date

5-29-2014 2:15 PM

End Time

29-5-2014 3:15 PM

Location

Ackerman (ACK) 141

Department

Mathematics

Session Chair

Michael Ward

Session Title

Pi Mu Epsilon Induction & Speaker

Faculty Sponsor(s)

Michael Ward

Presentation Type

Presentation

Abstract

Whether dealing with property, inheritance, revenue, or taxes, the question of how to divide “goods” (cake) fairly among a group of people is a ubiquitous problem.

At first glance, the question of dividing a cake fairly among n people may seem to pose no problems: just cut it into n equal pieces. But, while this might work for a homogeneous chocolate cake, consider a cake which is half chocolate and half vanilla, with sprinkles in one corner; that is, a cake where each player may value different parts of the cake differently.

While the problem of dividing one cake among several players has received considerable attention, the problem of dividing multiple cakes introduces new challenges, and, despite its usefulness in economics, has yielded little ground.

We consider a situation in which a player’s desired piece in the second cake depends on the piece he received in the first cake.

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May 29th, 2:15 PM May 29th, 3:15 PM

Cutting Cakes with Linked Preferences

Ackerman (ACK) 141

Whether dealing with property, inheritance, revenue, or taxes, the question of how to divide “goods” (cake) fairly among a group of people is a ubiquitous problem.

At first glance, the question of dividing a cake fairly among n people may seem to pose no problems: just cut it into n equal pieces. But, while this might work for a homogeneous chocolate cake, consider a cake which is half chocolate and half vanilla, with sprinkles in one corner; that is, a cake where each player may value different parts of the cake differently.

While the problem of dividing one cake among several players has received considerable attention, the problem of dividing multiple cakes introduces new challenges, and, despite its usefulness in economics, has yielded little ground.

We consider a situation in which a player’s desired piece in the second cake depends on the piece he received in the first cake.