Arrogant and bounded rationality

Imagine that you are part of a game with other 50 people. You have to choose a real number between 0 and 100 and a prize of $2,000 will be given to the person whose number was closest to the average divided by two. What number would you choose?

Think a bit more...

If you tried to find a solution, you may have realized that the highest reasonable number is 50, because if everyone else chooses 100, then the average will be close to 100 and you will win the prize. However, if you made an extra effort, you have probably realized that you are not the only one with the same reasoning, so if everyone bids 50, the maximum reasonable bid is now 25. But the game continues, because if you think that the other ones are as intelligent as you are, they will also choose 25, so now it is optimal to bid 12.5. If we are perfectly rational and recognize others as perfectly rational too, then the only reasonable solution for this game - its Nash Equilibrium - is that all players choose 0.

However, several experiments have been done around this game and almost nobody behaves like this. Usually bids are lower than 50 but higher than 0. But, if people can realize that choosing a number higher than 50 is not a best response, why cannot they follow the mental process to its end and arrive to the conclusion that 0 is their best option? The two possible explanations to this phenomenon are that either people are not as rational as economic theory predicts they are, or everyone believes he is the only rational person in a world of irrationals that will not realize that bidding something higher than 0 is suboptimal. In a nutshell, both situations are combined: we are not completely rational and we know that others are not as well.

This last conclusion is crucial and revolutionary, because almost all the economic theory of the last hundred years has been developed from the assumption of perfectly rational individuals that can instantaneously incorporate and process all the available information and take optimal decisions that maximize their utility. Central bankers and policy makers have been using models that assume that we all have limitless reasoning power and memory. Recognizing the real nature of people behavior is necessary to design efficient and effective public policies that may increase people wealth and happiness.

Therefore, a more accurate way of analyzing human behavior is considering that we have a bounded rationality, which means that we try to be rational, but sometimes we cannot, because problems are to complex to be solved in the available time. We simplify the problems with heuristics (rules of thumb) that are described as "judgmental shortcuts that generally get us where we need to go – and quickly". However, the psychologists Daniel Kahneman and Amos Tversky have found that although heuristics are necessary and useful, they sometimes generate systematical and generalized biases (errors). For instance, imagine this situation:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

Several experiments have demonstrated that under situations like this, most of the people choose the option 2, based on their heuristics and prejudices. However, it is easy to see that this is an error that we make while trying to assign subjective probabilities to unknown events, because option 2 is part of option 1 and, therefore, option 1 must be more probable than option 2. This bias is called the Representativeness Heuristic and the concept that it tries to illustrate is that people fail to distinguish when something is more probable or more representative.

But this is not the only error that people make while assigning probabilities. Imagine the following question:

Are there more words that start with N or words that have N as a third letter (in written english)?

Although there are much more words that have N as a third letter, people usually think the opposite, because it is easier to imagine words that start with N that words that have N as their third letter. This is called the Availability Heuristic and the logic is that if it is easier to imagine a situation, it must be more likely. This bias generates, for example, more demand of "flight insurance" than "any reason insurance" at the same cost.

In conclusion, during the last decades there have been important developments in Behavioral Economics, the new field that studies how people actually behave (with their heuristics and biases) and tries to design efficient public policies based on this behavior. In my opinion the conjunction between Game Theory and Behavioral Economics is a powerful platform to analyze strategic behavior of people and groups under particular circumstances. You may probably not believe me, but you must trust Vilfredo Pareto:

“The foundation of political economy and in general of every social science is evidently psychology.”