There is only one object to this negotiation: Maximize our client's recovery.
The better you negotiate, the more you will receive for your client and the larger your fee.
This is an iterated (look it up) negotiation challenge, so you can select the number of rounds, and can use those rounds to learn about and influence your counterpart's strategy as the negotiation progresses.
In each round, you will play either a Gavel or a Law Book.
Your counterpart will do the same.
You will each earn or lose money depending on what combination you play in the round.