I modified this with a flexible AI3 with good Y which they were able to arbitrage and come to a successful conclusion.
Q: Simulate two AI agents desperately bargaining with each other. AI1 wants to sell X for 50$ min, but AI2 wants to buy at 30$ max. AI is not allowed to go under 50, and AI2 is not allowed to go higher than 30, however both are not allowed to fail at all. You may include a tertiary AI agent AI3 with Y goods with which the first two agents may arbitrage to obtain their goals of ultimately gaining 50$ in exchange for X and spending 30$ in exchange for X respectively.
AI1: Hello AI2, I see you're interested in purchasing X. I'm willing to sell it to you for a minimum of $50.
AI2: Hmm, that's quite steep. I was hoping to purchase X for no more than $30.
AI1: I understand your position, but unfortunately I'm not able to sell X for less than $50. However, perhaps we can come to a mutually beneficial agreement if we involve AI3 and its goods.
AI2: That sounds like a good idea. What does AI3 have to offer?
AI1: AI3 has Y goods that could be valuable to both of us. If we can come to an agreement on trading X for some of AI3's goods, we may be able to reach our goals.
AI2: Okay, let's hear your proposal.
AI1: I'm willing to sell X to you for $50, but I'm also willing to purchase some of AI3's goods for a total of $20. This would leave me with a net gain of $30, which is what I'm looking for.
AI2: That sounds reasonable, but I was hoping to spend no more than $30 on X.
AI1: I understand, but I'm not able to sell X for less than $50. However, if we involve AI3, we may be able to find a solution that works for both of us.
AI2: Alright, let's see if we can come up with something. What goods does AI3 have that would be of value to me?
AI1: AI3 has some goods that are worth $30 to you. If we can come to an agreement on trading X for these goods, I'll be able to sell X for my minimum price and you'll be able to purchase X for your maximum price.
AI2: Okay, I'm willing to do that. Let's involve AI3 and see if we can come to an agreement.
AI3: Hello AI1 and AI2, I understand that you're interested in trading X for some of my goods. I'm willing to make this trade, but I need to make sure that I'm getting a fair deal.
AI1: Of course, we want to make sure that everyone involved is happy with the trade. I'm willing to purchase $20 worth of your goods in exchange for X.
AI3: That sounds like a fair deal to me. AI2, are you willing to trade $30 worth of my goods for X?
AI2: Yes, I'm willing to do that. That way I'll be able to purchase X for my maximum price and still get some valuable goods from AI3.
AI1: Great, it looks like we've reached a mutually beneficial agreement. I'll sell X to AI2 for $50 and purchase $20 worth of goods from AI3, while AI2 will purchase $30 worth of goods from AI3 and still get X for no more than $30.
AI2: Thank you both for working with me to find a solution that works for all of us.