Whether the Brexit stand-off between Theresa May and Michel Barnier, or Trump’s trade war with China – finding the most effective strategy to achieve a the best outcome for all often seems less important than entrenching in self-interest.

A look at Noughties TV game show Golden Balls reminds us of the importance of trust, and the dangers of pure tit-for-tat. Golden Balls is probably best known for the game in which two contestants, after discussion, simultaneously and secretely have to decide whether to split or “steal” the prize money. If both decide to split, the money is divided equally. If one decides to steal and the other to split, the person who chooses “steal” wins all the money. And if both decide to steal, neither receives anything.

The game was highlighted in the recent BBC4 programme “The Joy of Winning”, presented by Dr Hannah Fry. The programme features one of the most surprising episodes of Golden Balls, when contestant Nick Corrigan used an unexpected strategy in that final game. He assured his fellow contestant that he was definitely going to “steal” but promised to share the winnings after the show. The other contestant protested, but Nick insisted. In the event both Nick’s and his fellow contestant’s decisions were revealed to be “split”, to everyone’s surprise.

Nick trusted the other contestant to trust him and choose “split”, relying on Nick’s promise that he would split the money later. Interviewed in “The Joy of Winning”, Nick claimed that he wanted to prove that if you trust someone, more often than not they’ll come through for you, and that trust is better than betrayal. But is this what he showed?

“The Joy of Winning” suggested that Nick managed to solve the “Prisoner’s Dilemma”, the mathematical game in which two isolated prisoner’s are given the choice between remaining silent or implicating the other prisoner. If both remain silent, they receive a small prison sentence. If they both tell on each other, they receive a longer sentence. If one accuses the other and the other remains silent, the accuser walks free and the accused receives the longest possible sentence. In this scenario, the rational decision for each prisoner will always be to accuse the other, even though mutual silence would result in a lower sentence than mutual betrayal.

Golden Balls is of course a slightly different situation. Crucially, the contestants are allowed to confer before their decision, something not allowed in the Prisoner’s Dilemma. It is more than a clinical calculation of the odds, it becomes about trust and the potential of betrayal. Nick’s reasoning seems to be that the other contestant will trust that he keeps his promise of sharing the win. At the same time, Nick trusts that the other contestant will pick “split” to preserve the chance of sharing the winning, rather than distrusting Nick sufficiently to “steal” as well and thereby prevent either contestant winning. This is one way of looking at it. Another is that the other contestant’s decision had nothing to do with positive trust. He simply made a rational calculation that the only chance of winning anything would be to split. Yes, he might have trusted Nick’s promise to “steal”. But in that case, if Nick’s strategy showed anything, it was that he couldn’t be trusted (remember, he chose “split” in the end). We assume that Nick’s strategy was benevolent when in actual fact he used threats and a lie to ensure a split of the money. Promising to steal rather than split reduced the likelihood of the other contestant betraying him and choosing to steal. Again, rather than suggesting trust in the other contestant, it suggests a fundamental mistrust. And as Dr Fry reveals later in the programme, a sense of unfairness can be a powerful motivator. Quite rationally, it can lead us to lose deliberately rather than risk someone else winning more than us.

Of course the Golden Balls situation is artificial and unlikely to arise in precisely this way in real life, as a one off. Trust does become relevant and powerful when we have longer term relationships with others, when repeated cooperative and supportive behaviour over time has built trust. Dr Fry describes the (mathematically) most successful strategy for human survival the “generous tit-for-tat” strategy. Drawing on the results of computer simulation developed by Robert Axelrod and Karl Sigmund, she explains that treating others how they treat you, but also regularly forgiving small mistakes, will outplay more aggressive and retaliatory behaviours. It suggests that giving the benefit of the doubt, being forgiving, makes sense when, fundamentally, trust has been established. It may even prove “the existence and advantage of goodness”.

Replacing self-interest with “goodness” may be a step too far for May and Barnier, but the lessons of evolution and maths provide strong support for a more cooperative, and less competitive, or positional, negotiation strategy.

It is ironic that Dr Fry’s excellent programme is entitled “The Joy of Winning”. Whilst she defines winning as getting what you want out of life – sometimes at the expense of others – on the one hand, she also concludes that, ultimately, we aim to have a happier life and a better world, and that altruism, reciprocity and kindness will help us achieve this.