I have devoted most of my life to economic theory and game theory. I believe that I would like to do some good for humankind and, in particular, for the people in Israel, the country where I was born and where I make my home. I would like to make an impact and redress injustices. Ostensibly, all this should motivate me to utilize my professional knowledge in order to bring some relief to the world. But, the thing is, that is not how I feel.
I probably should start again with an answer to the question: What is game theory? Game theory has a sexy name, but it is actually no more than a collection of concepts and models about rational human behavior in strategic situations – that is, in situations in which the considerations of a rational player depend on how he assumes other players will behave. The rational player must step into the shoes of the other players, who also face a similar task. This circuitousness is the source of the complication (and the interest) in game theory. Game theory tries to inject content into the concept of rationality in a context in which the meaning of rationality is unclear.
Here is a typical game theory situation called the Hide and Seek Game: A cruel ruler can hide in one of four palaces (marked 1, 2, 3 and 4) positioned along a river that flows from west to east. Palace 2 is painted gold, while the three other palaces are white. The seeker can attack only one palace. The rational hider will try to hide in the palace he believes the seeker is least likely to attack. The rational seeker will attack the palace he believes the hider is most likely to choose as a hideout. Game theory asks: How do the hider and seeker construct their beliefs in a way that is consistent with the assumption that their opponent is also rational? Game theory’s “prediction” about the outcome is that the seeker’s chance of catching the hider is one out of four (25%).
A nearly magical connection
The heart of game theory is not empirical science. It does not study how people actually behave in strategic situations. It is doubtful whether it is even possible to generalize about the way people will behave in a situation like the Hide and Seek Game. After all, people are diverse. There is experimental evidence indicating that among students who play a virtual game of Hide and Seek, about 40% of the hiders and seekers choose the white Palace 3 in the center; about 25% choose the gold Palace 2, while the rest (35%) are divided between Palace 1 and Palace 4, located at the two extremes. In these experiments, the seeker has a 30% chance of finding the hider – that is, a significantly higher likelihood than the 25% “predicted” by game theory. It is reasonable to assume that similar results would be found among this newspaper’s readers, but the figures would change after the readers become aware of this fact. And this, of course, reflects a central difficulty in the ability to predict, a difficulty that characterizes social sciences in general: People, unlike rocks, flowers and butterflies, listen to those who make predictions.
Game theory is written in a mathematical language. This offers some advantages: The formal language demands precision, allows for the removal of erroneous associations and thoroughly scrutinizes assertions. Personally, the nearly magical connection between the symbols and the words in game theory is what captivated me. But there are also disadvantages: The formal language greatly limits the audience that really understands it; the abstraction blurs factors that natural thought takes into account and the formality creates an illusion that the theory is scientific.