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MACS 42 b. Teoria e pratica dei giochi. Part 2. Several examples of Nash equilibrium could be cited. A classic one is the prisoner’s dilemma. We have two prisoners who have to choose whether to confess or not to confess. If one confesses and the other does not, the first one earns his freedom and the second one 10 years in prison (and vice versa). If both confess, they each get 5 years. If neither confesses, they each get one year in prison. In this case the Nash equilibrium occurs if both confess, because in the best case they will get out immediately and in the worst case they will serve 5 years. This is not an optimal solution, but the choice not to confess would be risky: in the best case 1 year, but in the worst case even 10 years. In technical terms, we would say that by confessing the two prisoners have decided to maximise the pay-off. Another example, explained by Ken Binmore in his book Game Theory and called ‘battle of the sexes’. Let’s imagine two guys, let’s say Alice and Bob, who have to decide whether to go to see a ballet show or a boxing match. She prefers ballet, he prefers boxing, but they both prefer to go out together rather than go out alone. The problem is that Alice and Bob do not have the possibility to communicate their decision to each other, so they will have to make it blindly, imagining the other’s decision: if they succeed, Nash equilibrium occurs, and the two will win their prize of spending the evening together, even if one will be happier than the other. If, on the other hand, they do not guess the other’s choice, they will both have lost (more or less well, depending on whether they chose to do the thing they liked or the thing the other liked): the worst case is in fact that Alice goes to see boxing and Bob the ballet. Another example of Nash equilibrium is James Dean’s tragic ‘chicken game’ in Rebel Without a Cause: if both competitors slow down, they realise Nash equilibrium, neither of them wins but they save their lives. If neither slows down, they both die. If one slows down and the other does not, the one who slows down loses badly (he is the chicken) and the other wins. Finally – as Bertrand Russell observed – the Cold War itself had the characteristics of a Nash equilibrium because neither power was interested in resorting to atomic gambling. Here is an article that tried to apply this theory to the economic crisis in Greece in 2015. The fact that, as recounted in the film A Beautiful Mind, Nash’s first idea for equilibrium came from observing the dynamics of courtship is particularly audacious because it is precisely in this field that human behaviour is less rational and therefore less predictable than ever. But certainly passions always influence our choices in a more or less marked way. This has already been observed by many philosophers in the past, and led Schopenhauer to say that we live in the worst of all possible worlds, David Hume to say that reason is ‘the slave of the passions’, and Franco Battiato to write the song L’animale. If human behaviour were completely rational, game theory would explain everything; conversely, if human behaviour were completely irrational, game theory would explain nothing. In other words, it explains what would happen if all the parties involved acted rationally, which can be more or less close to how they actually act. Conflict games are called ‘zero-sum’ games, meaning that there is a winner and a loser, mors tua vita mea. Sometimes in life there can be conflict situations and therefore zero-sum games, but this happens more rarely than we think. Typically, life is not a zero-sum game. The real John Nash can be heard in this long documentary in which he explains the subject in simple words. John Nash is the revolutionary mathematician who applied game theory to economics, and who defined the Nash equilibrium. His personal story is also incredible, for better or for worse. Then there are some notes for engineering management students that deal with the same subject, but in a more technical way, and can be read in pdf here. They require skills that I don’t have at the moment: it’s a good incentive to study maths! In another scene from the film A Beautiful Mind, young Nash and his university friends at Princeton are playing Go. It is one of the oldest known games, having originated in China over 2500 years ago. The rules of Go are very simple, but because of this, the possible variations are countless. To start getting familiar, I can watch a few lessons, and some videos of commented games. At the beginning of the comedy Crazy Rich Asians (2018), the protagonist Rachel Chu – a young economics professor at New York University – gives a lesson by playing poker with an assistant to demonstrate that the key is “to play to win, not to avoid losing”.