An interesting game theory experiment from 2001 appears to show that women find it very easy to come to agreements with other women; but men are far readier to accept offers from women than from other men. The two effects are noteworthy, though painting the woman/woman effect as "solidarity" seems a bit odd. It's more likely that they understand each other, and have similar desires to come to agreement; whereas men, who understand each other, want to compete.
By the same token, "chivalry" is the wrong term here; this tendency describes all men who participated. It would have been very great good luck to gather only chivalrous men into the study!
When a woman is his partner in the game, however, a man becomes much less competitive: he is ready to accede to her requests almost at the same rate that women agree to accept/agree with either men or mixed groups. Men facing other men, however, accept offers only if they are much more generous.
The graph on page 184 is the main thing, I think. It shows that actual results are fairer in men/men pairings; but agreement is far more common in female/female pairings. That may mean that women are more interested in agreement than fairness (or gain); but it also may mean that men are more willing to resist authority if they feel it is not treating them fairly. After all, the proposer is in the position of authority where the resource division is involved; all the respondent can do is accept or reject the proposal. Men would rather punish unfair actors than seek agreement, even if that means gaining nothing rather than gaining an unfairly small amount.
Unless, that is, they are receiving the proposal from a woman: then, they're much readier to be treated unfairly!
Another way of saying that, though, is that they are more willing to accept female authority -- fair or unfair -- than they are to accept unfair male authority. From another man, they will only accept fairness.
This only treats initial acceptance, of course. One might later resent being treated unfairly, even if this proves that -- in some cases -- one is readier to be treated unfairly. It's also interesting that both men and women are readier to be treated unfairly by women than by men.
Chivalry & Solidarity in Game Theory
"Chivalry & Solidarity in Ultimatum Games"
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