Fair Division Method

A fair division method is a procedure that can be followed that will result in a division of items in a way so that each party feels they have received their fair share. For these methods to work, we have to make a few assumptions:

The parties are non$-$cooperative, so the method must operate without communication between the parties.

The parties have no knowledge of what the other players like $($their valuations$).$

The parties act rationally, meaning they act in their best interest, and do not make emotional decisions.

The method should allow the parties to make a fair division without requiring an outside arbitrator or other intervention.

Fair Share

When $N$ parties divide something equally, each party's fair share is the amount they entitled to$.$ As a fraction, it will be $\frac{1}{N}$

Suppose that $4$ classmates are splitting equally a $$27$ pizza that is half pepperoni, half veggie that some else bought them. What is each person's fair share in dollars?