When Maths Doesn't Work: What we learn from the Prisoners' Dilemma

Game Theory is a branch of mathematics which tells us how to outthink an opponent or competitor. The Prisoners' Dilemma is a paradox in which knowledge of Game Theory is dangerous: the sophisticated mathematician comes off disastrously worse than the ignoramus.

For many years, the Prisoners' Dilemma was something of an embarrassment to the subject. A rigorous mathematical argument gives a ridiculous conclusion, and there seems to be no way round it. Mathematics appears to justify selfishness.

But the power of the computer has changed everything. Recent work has used the Prisoners' Dillemma to tackle one of the big problems of evolutionary biology - in a Darwinian world, how does co-operation arise? Mathematical modelling and computer simulation use the Dilemma as the basis for a rich and provocative examination of the evolution of unselfish behaviour, and has thrown light on the generous altruistic behaviour of bats, fish, animals and people. We'll learn why it pays to be "nice", with examples from the First World War battlefield and the Champions League football field.

It is now at the heart of mathematicians' exploration of co-operation. We're gaining insights into the nature and importance of trust, and why reputation matters so much. This mathematics may help us understand how we can avoid calamitous climate change.