Today’s Labour party is divided and angry. 72 hours seldom pass without the MPs or the leadership suggesting the others can’t be trusted. If no one is happy, surely some sort of change must be around the corner? In the short run, the MPs have the power: they could create a crisis for Jeremy Corbyn tomorrow while he can only get rid of them over time. So one of the few remaining interesting questions you can ask in Labour politics is, when will they act?

This is the sort of situation game theory was invented for. By describing different choices available to people in precise terms, the mathematician John Nash, found he could explain suboptimal equilibria, i.e. situations that stay the same even though everyone is unhappy. Take a town that depends on a single road, maintained through voluntary donations. Nash’s theory says the road will fall into disrepair, even though everyone would be better off with a decent road. No one will pay the whole cost of something themselves when the benefits are shared amongst everyone in town. If they donate, others will use the road without donating. So until the rules change, through the creation of a compulsory tax for example, the road gets worse and so does life in the town.

The parliamentary Labour Party faces the same challenge. Most think that the party as a whole would be more successful with a different leader. But all know that the leaders of any mutiny would become the prime targets for every furious deselectivist on Twitter or in their Constituency Labour Party. The collective benefit of explicitly challenging Corbyn’s leadership could be as big as you like; so long as the individual gains are less than the individual costs, the temptation will always be for each MP to wait for their colleagues to step up first.

The same dynamic may even work the other way: it’s arguable that unity behind Corbyn would be more successful than the current shambles. But suppose you are an MP sat in Strangers’ Bar and a journalist asks you what you think. The benefits of unity are collected, while the costs – having to defend something you think ludicrous – are paid by the individual MP. And besides, the journalist can just move down the bar and get the same quote from another MP.

So trying to challenge Corbyn would be hard, as would trying to offer a full-throated defence. The easier path is more popular: to always complain but never oppose. It's not optimal for anyone but it appears to be the position most MPs are settling into.

But suppose, eventually, some MPs decide that they have nothing to lose. Behavioural economists suggest that people behave differently, taking more risks, when it looks like they are in a downward spiral. But still the question is when. After May’s elections? After the referendum? When Labour lose a by-election?

If you want to predict when the parliamentary Labour Party will finally take Corbyn on, look to an experiment run on students at the Massachusetts Institute of Technology. Some of the students were allowed to pick their own deadlines for their essays, while others were given fixed deadlines. The first group had more freedom, but worse grades. The same problem causes people to save too little and eat too much. Tomorrow is always a slightly better day to start doing the right thing so we tell ourselves we are waiting for the right moment when, in fact, we are waiting for the last moment. However bad things look in the polls, even the prospect of losing their seats in the future may not motivate MPs to act today.

Instead, the situation today - how bad it feels right now, compared to how bad it would be to be attacked, is likely to be more important. We are a long way from reaching the point where open rebellion looks like the least uncomfortable option for an MP. So even Corbyn's firm opponents may delay in perpetuity, unless their hands are forced.

So an impasse but not a stalemate. The MPs started losing power the moment that nominations for party leader closed. The boundary review and the changing makeup of the party membership will weaken them further. While Corbyn’s team might prefer loyalty, they will settle for rows on the issues, like Trident, that energise their supporters. Every week the PLP meeting will produce some quotes about Corbyn and his team, sometimes cruel, sometimes effective. And it will mark another week that Corbyn has been in charge.