The assumption that “equal monetary EV” is the definition of “fair” is questionable. In fact, any wager between 21% and 39% (narrower if transaction costs and risk-of-ruin are included) is fair from the standpoint of “ask participants prefer to make the bet vs declining”.
If you do want to make it “fair” in terms of equal benefit to both, you probably need their utility-of-marginal-money calculations. If Alice really needs the money, it’s not “fair” for Bob to demand half of the monetary expectation.
There’s also the fairness question of whether they are equally rational and well calibrated and have the same relevant information (hint: Aumann proved they don’t).
The assumption that “equal monetary EV” is the definition of “fair” is questionable. In fact, any wager between 21% and 39% (narrower if transaction costs and risk-of-ruin are included) is fair from the standpoint of “ask participants prefer to make the bet vs declining”.
If you do want to make it “fair” in terms of equal benefit to both, you probably need their utility-of-marginal-money calculations. If Alice really needs the money, it’s not “fair” for Bob to demand half of the monetary expectation.
There’s also the fairness question of whether they are equally rational and well calibrated and have the same relevant information (hint: Aumann proved they don’t).
Yes, fair here means that their subjective EVs are equal. The post referenced in the sibling comment calls it “Even Odds”, which is probably better.