Game theory generally says offer as small as possible. Even 1% is better than nothing. Sadly this solution generally ignores payouts outside the game. We are pretty hardwired to have feelings related to fairness, and that changes the payout equation a lot.

I used to annoy one of my freshman econ professors because I would “stubbornly” (from his view) not play along with game theory thought experiments. His claim was I was being irrational not to accept some theoretic dollar amount, and my response was that I would gain more than said dollar’s amount from seeing my fellow students profit more. (imagine games intended to evoke prisoner’s dilemma outcomes, like you get $100 dollars if you say yes, all 200 students get $1 if you say no).

This was a period when behavior economics was starting to be really taking off, so I wonder today how those lessons are taught, because it is not at all irrational to value things outside of money.