Complex Negotiation: multiple parties and long-term deals

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I'm learning "Complex Negotiation: multiple parties and long-term deals" on The Future Market. Lesson 1: "Mapping a multi-party negotiation".

What the lesson teaches:
- Before this course: Negotiation Skills (course 2.14.2), which came after Negotiation Basics (course 2.14). You already know the Me, Them, Process sheet, interests behind positions, logrolling, shrinking concessions, objective criteria and the written recap. This course adds more parties, longer time and harder conflict.
- Harvard's Program on Negotiation (PON) says that in a multiparty negotiation, paying close attention to coalitional strategies and the changing BATNAs of all parties helps negotiators pursue their interests.
- PON also notes that power differences can be made worse in multiparty talks.
- Useful questions for a map: Who is at the table? Who is not at the table but must approve? Who can block the deal? Who will carry out the deal afterwards?
- A person at the table may only be a messenger. Find out who has the authority to say yes.
- Each party has its own interests and its own BATNA. When one party leaves or joins, everyone's alternatives can change.

The exercise I'm working on:
Draw a party map for one group negotiation. Mark the decision maker, the blockers and each party's likely BATNA.

I'm stuck. Please:
1. Explain the main idea in plain, simple words with one everyday example.
2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step.
3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.

I'm a parent helping my child (about 8 years old) with a lesson called "Mapping a multi-party negotiation" from the course "Complex Negotiation: multiple parties and long-term deals".

Here's what the lesson says:
Sharing a pizza with one friend is easy. Sharing it with six friends, a parent who pays and a cousin who may join later is harder, because everyone wants something different. First you draw who is at the table.

The activity:
Draw a party map for one group negotiation. Mark the decision maker, the blockers and each party's likely BATNA.

Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words.
Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.