The first “ultimatum game” was conducted by three researchers at the University of Cologne in 1982. Two players, unknown to each other previously and unable to communicate during the game, were asked to split a pot of money between them.

The first player got to choose the division. The second player got to accept or reject the division. But if it was rejected neither player would get anything.

According to the axioms of “rational” economic choice the second player would be expected to accept any proposed division of the pot so long as she or he received more than zero. Something is, after all, worth more than nothing. And which rational person would choose nothing over something?

But that was not the result the researchers found when they ran this game multiple times with different subjects. On the occasions when the first player divided the pot less than equally the second player often reacted badly.

“Subjects will often rely on what they consider a fair or justified result,” they wrote. “The typical consideration of player 2 seems to be: ‘If player 1 left a fair amount to me, I will accept. If not…I will punish him by choosing conflict’ ”.

This was the first study to provide compelling empirical evidence that people often value “fairness” just as much as money – and that that the principle of fairness can actually trump financial considerations. A great many other empirical studies over the past three and a half decades have supported the finding. Ultimatum games played and observed in different countries, different cultures, among different professional groups, have all pointed in the same general direction.

And this week we have had a vivid real-world confirmation of it with Carrie Gracie’s resignation of her job as China editor of the BBC on the grounds that she was being paid less than her male counterparts.

Gracie says her bosses at the Corporation offered her a £45,000 pay rise, taking her salary to £180,000, when she complained about the disparity and demanded redress. But the pay rise would still not have meant gender pay parity, so she resigned and went public with her frustrations, landing the BBC in an exquisite public relations nightmare.

As for Gracie, she will come away, not quite with nothing (she will remain employed in a more junior capacity at the BBC), but with considerably less money than she could have had if she had accepted the offer. “I didn’t want more money. I wanted equality,” as she put it. The principle was more important than the money.

It may be naïve to expect BBC managers to be familiar with the scientific literature on ultimatum games. Yet one presumes they are pretty experienced in staff negotiations about salaries. So why did they get it so disastrously wrong on this occasion?

The answer is that they were probably doing what they have done in the past: addressing the case of a valued staff member unhappy about money by offering them a bit more cash.

 But of course the terms of this negotiation were very different. As in the ultimatum game, both sides had full information. Ms Gracie knew, roughly, what her male counterparts were being paid because the Government had forced a high level of pay transparency on the Corporation. £45,000 is a lot of money: more than the average UK wage. But Mr Gracie was able to put it in context

 There is a lesson her for bosses not just at the BBC but everywhere. An informed workforce on matters of relative pay levels is one that is liable to put more of a premium on principles. They will be less amenable to being bought off. Games of what Gracie terms “divide and rule” of the staff will not work in the way they might have in the past.

 The Government’s deadline for all firms with more than 250 staff to reveal their overall gender pay gaps will fall in April. This will even out the informational playing field between staff and managements in larger companies to some extent. But not much. The breakthrough in the BBC case was allowing people doing similar work and with similar levels of seniority and experience to work out the gap between them. Aggregate firm-level gaps will not facilitate this individual-level comparison.

 The best hope for those suffering from wage discrimination – and the worst nightmare for bosses guilty of discrimination – is that the aggregate gender pay disclosure requirement is merely the beginning of a new comprehensive era of pay transparency. For information really is power.