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Teoria e pratica dei giochi

In the past I despised games, all games, any kind of games. Because they were stupid. Because there is no use wasting time on frivolous pastimes, I told myself, when there are so many serious problems to think about. So I devoted my time and energy to reading books. I was better than the other kids who were only interested in winning.

Now I can’t say whether this conviction of mine was entirely honest, but the fact is that when I found myself in one way or another playing a game – you’re always playing something in life, whether the game is explicit or not – I wanted to win, too, and I was very rosy if I did. Winning or losing a game was the difference between a good day and a bad day, between a happy or unhappy time, between success and failure.

So, to be honest, the reason I hated games was not their stupidity, nor my lack of interest in the competition; on the contrary, the outcome of the competition was so important to me that I could only accept it if victory was guaranteed. I was too afraid of losing to enjoy the game itself, and I must say, a residue of that fear still lingers today.

After a long and not very playful adulthood, one day I enrolled in a master’s course to teach Italian to foreigners: and lo and behold, the first thing they told me was that the best way to do it was through play. I resisted this idea for a long time, then I accepted it marginally and laterally, passing through fun rather than actual play, and finally I took a liking to proposing as many games as possible, and to play as many cognitive processes related to linguistic structures as possible.

Over the last two years, I have discovered improvisational theatre, and with it the idea of non-competitive play and the make your partner look good rule. In short, after all these experiences, I have not only accepted the existence of games, but I consider them a privileged vehicle for learning (I use them in my work), for getting to know other people (a large part of my social life passes through them), for personal growth, for training our emotional intelligence, imagination and creativity.

The price to pay, apparently, is that you can lose. But this is actually the most precious gift that the game can leave us: learning to lose means becoming strong, adult and self-confident. The insecure ones are not the ones who lose, but the ones who do not have strong enough shoulders to bear it. When you understand that, losing is beautiful. Unfortunately, my deep-seated ego will never agree with this, so I feel the need to play, play, train myself to have fun, risk, and defeat, until the signs of anxiety and stress fade away.
Playing brings with it a lot of paradoxes: it is only when we get rid of the fear of losing, in fact, that we start to give our best to win. And why? Because when we are all motivated to win, and freed from the fear of losing, the game becomes spectacular.

Only great stupidity can lead us to consider a game ‘stupid’: the complexity of the variants involved, on an intellectual, cognitive, emotional, psychological and philosophical level, is such that only a highly evolved discipline can attempt to account for it. This discipline is called game theory, and those who deal with it ‘analyse the individual decisions of a subject in situations of conflict or strategic interaction with other rival subjects (two or more) aimed at each subject’s maximum gain’. One could say even more briefly: every time human beings interact with each other, they are playing something.

In the introduction to his book Game Theory, Ken Binmore notes that everything can be played, and even if the game does not completely capture reality, it can come close, allowing us to understand and accept it. For example, drivers in traffic are playing the driving game; eBay auctioneers are playing the auction game; a company and a trade union negotiating the terms of new contracts are playing the contract game; political candidates in an election choosing their government programme are playing the election game; the shopkeeper deciding the price of cornflakes is playing the price game.

I am reminded that when I was a teenager I saw a film called Singles, set in grunge-era Seattle. For me, who had a lot of emotional problems, being told that love was a game had an encouraging and downplaying effect. But at the time I was inclined to understand the word ‘game’ as ‘silly’, not very serious, and consequently if love was a game it was silly. Obviously this is not the case, play is a very serious thing and perhaps only today am I able to understand the true meaning of that slogan.

In what sense then is love a game? In the sense that it can be rationalised, and therefore theorised. In this rich introduction to game theory, a fragment of the film A Beautiful Mind is shown with an example of game-playing applied to the subject: here the young and brilliant John Nash and his university friends at Princeton, while they are in a bar one evening, see an incredibly beautiful girl approaching them together with some friends. The boys immediately prepare to compete with each other to win her over, and one of them in fact comments: as Adam Smith, the father of modern economics, teaches, one must accept competition because individual ambition serves the common good. But Nash disagrees: “Adam Smith needs to be revised”, he objects, and explains that “if we all try for the girl, the only result is that we eliminate each other”. And this little practical case contains the germ of what will become the basis of the entire game theory, namely Nash equilibrium. Which is not a form of zero-sum game, but a collaborative one. No player can win by thinking only of his own strategy, but must take into account those of others, to which his own success will be bound.

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”.

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