Thought Experiment II
March 1st, 2008
I recently posted a thought experiment where you had to try and find 2/3rd of the average number.
I said that you can assume people’s guesses are uniformly distributed. I think that’s a reasonable thing to assume, and hence the average of all the numbers chosen would be 50. 2/3rd of 50 is 33.
Simple enough, but everybody else also knows this; they’ll all choose 33. But if everyone else chooses 33, 2/3rd of the average is actually 22. And so on… the logical answer to choose would be 0.
This question links to game theory, where mathematics is used to try and discover the behaviour of individuals where the behaviour chosen will depend on the behaviour exerted by other people. In some ways, this can also be a criticism of economics - economics makes certain assumptions which would predict everyone would choose 0. But in the real world, it is unlikely everybody would choose 0.
Another one
One of my friends sent me this: “I’m going to give you £500 on a certain day this week but you won’t know it’ll be that day in advance.”
You can’t get the money on Saturday because if you haven’t received £500 by Friday, you’ll know the money will come on Saturday (the last day of the week). But it can’t be Friday either; if you haven’t received the money by Thursday, you’ll know that it’ll come on Friday. And so on.
Its nice to see people using game theory, but using it as “a criticism of economics” is too simplistic. Yes, the above games assume rationality on behalf of all players but is this assumption too strong? The general conlusion should be no. Game theory and economics in general - though not strictly necessary in all cases - do place assumptions of rationality on models that are solved under various Nash equilibria conditions. If one were to neglect such an assumption the model is likely to have a large and possibly infinite number of solutions which is unwanted. If you really want completely acurate - or realistic model - then by all means try to model it. Without such basic simplifications one could not even begin to solve such a simple model as your former example.
A few examples of such would be insurance markets and auctions. In both of these models we assume that agents are rational - although no agent may have complete or perfect information. In the insurance market we _could_ assume that firms and customers were not rational but this would yield nothing but pointless information. The simple addition of rationaility allows for all agents to maximise their own utility in a logical fasion. This analysis can be generalised to almost all game theoretic models with the most fanous example being that of Akerlof, G. “The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism,” Quarterly Journal of Economics, 1970. While not strictly a game theortic paper it gives a good example of how such simplifying assumptions can be applied in a variety of cases and produce useful, and intuitive results.
It seems like that’s what I was saying in response to the first thought experiment post… The assumption that “all people are rational” isn’t realistic, and is thus why I wouldn’t consider zero to be a valid answer to that first thought experiment (in theory, of course it is, but factor in human rationale, and the problem becomes less about game theory than psychology in general).
Harold: You’re very correct but I think the fact that one needs to make assumptions in order for a model to work or to even develop a model does not make that assumption valid. I think economics and game theory make reasonable assumptions in order to develop their models and predictions but I think this does highlight some shortcomings in the model.
Andrew made some good points - there are lots of other factors such as human psychology to factor in. Not to mention that in the real world, there probably isn’t going to be “no knowledge” of the choices of others. It might be interesting to actually run this experiment on the internet, but if someone can find out the number entered by any other person it’ll instantly affect the results of the study.