Thank you, this has prompted some very useful thoughts.

you can see a sort of noblesse oblige in others which leads to huge charitable donations and voluntarily forgoing chances to improve their position

This feels close to my situation. I come from a high-privilege family with a long tradition of self-sacrifice and doing good works.

I thought of a theory to explain my situation. Part of my problem is not really wanting to win in negotiations. I do want to win, just not as much as I want to avoid feeling socially awkward and grasping. When the negotiation stakes are small for me, I would rather spend more money and feel better. When the stakes are negligible for all, like in games, I play to win. When the stakes are very high for me, it would be rational to negotiate hard, but I don't do that as much as I want to, out of habit learned on smaller stakes and because I do hyperbolic discounting and weigh feeling awkward now higher than losing lots of money long term.

The stakes in the role play negotiation were negligible, but I still did badly. However, it felt real enough while I was doing it. I was feeling very awkward.

Exposure and deliberate practice seem like good ways of reducing the awkwardness. Another line is to work on the hyperbolic discounting. I could think of the decision in Timeless terms: "I'm making the awkwardness vs profit decision for all similar negotiations." Or I could think what I would advise a needy friend to do.