Sarah and Max must decide how to split up $8$ cookies. Sarah $($we$\text{'}$ll call her player $1)$ makes a proposal to Max $($we$\text{'}$ll call him player $2),$ of how many cookies each of them should receive. We assume that each kid is trying to maximize the amount of cookies they receive, and that they must follow the rules below:

If Max accepts the proposal, they split the cookies according to that agreement.

If Max doesn't accept the proposal, he tells their dad. Their dad will eat $4$ of the cookies and then split the rest evenly.

Assume that if Max is indifferent between accepting and rejecting, he will always accept the offer.

How many cookies will Sarah offer Max?