Suppose Players 1, 2, and 3 View a Cake as Shown

question 47

Essay

Suppose players 1, 2, and 3 view a cake as shown below and that all cuts are vertical. Illustrate the envy-free procedure for n = 3 (yielding an allocation of part of the cake) by following the steps below:
a) Provide a total of three drawings to show how each player views a division of the cake by player 1 into three pieces he or she considers to be the same size or value. Label the pieces A, B, and C.
b) Redraw the picture from player 2's view and illustrate the trimmings of piece B that he or she would do. Label the trimmed piece $B ^ { \prime }$ and the actual trimmings T.
c) Indicate which piece each player would choose (and what he or she thinks its size is) if the players choose in the following order: player 3, player 2, player 1, according to the rules of the procedure.

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Definitions:

Secondary Liability

A legal responsibility whereby one party is held liable for the actions of a third party, typically in copyright or partnership cases.

Unauthorized Signature

An unauthorized signature is a signature made without the express permission of the person whose name is signed, often considered fraudulent or voidable.

Negligence

A legal concept where an individual fails to exercise a reasonable level of care, resulting in harm or damage to another person.

Principal

In law, a principal can refer to a party who grants authority to an agent to act in their stead; in finance, it can refer to the original amount of money invested or loaned, before any interest.