Now I'm learning Java to write a program that can conduct the
negotiation between two agents and reach a Pareto optimal solution. The
problem is that I don't even know the first step to start. Could anyone
give me some instructions that may help to develop the algorithm? Thank
you very much. Below is the subject:

A and B are both rational agents.
Agent A attempts to maximize the utility function:
F(X,Y,Z) = 3X - 2Y + aZ -10T
Agent B attempts to maximize the utility function:
F(X,Y,Z) = 4Y - 2X + aZ -15T
a is some uncertain real constant between 2 to 4.
T is the number of rounds they reach agreement.
Let assume the domain has the 5 facts that
1. X is greater than 20 and is upper bounded by 500
2. Y is greater than 30 and is upper bounded by 600
3. Z is greater than 50 and is upper bounded by 400
4. X + Y = 500
5. Y + Z = 700
Both agents A and B have a limitation of 10 times of negotiation rounds
(i.e. each can propose 10 times at most) to reach an agreement.
Each time they cannot propose the same offer that has been proposed by
himself or other before. The minimal decrement or increment for X, Y,
and Z are 1, 1, 1 respectively.
A and B do not know other agent's utility function and they don't know
other have the time bound either but they all know the facts 1 to 5.

Thank you.


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