Thursday, August 28, 2008

Aumann on rule optmality vs act optimality

I was watching Robert Aumann give a talk on rule vs act rationality, and my first thought (after, 'I bet he's Jewish') is that it brought forth a profound point. A decision may make no sense as an act, but as part of a rule, and this makes sense.

The ultimatum game is an experimental economics game in which two players interact to decide how to divide a sum of money that is given to them. The first player proposes how to divide the sum between themselves, and the second player can either accept or reject this proposal. If the second player rejects, neither player receives anything. If the second player accepts, the money is split according to the proposal. The game is played only once, and anonymously, so that reciprocation is not an issue.

Most people reject an offer less than 20% of the pool. Aumann sees this as both irrational in the act, but rational in the general sense that one does not want to appear a chump. The rule overrides our act rationality because humans have evolved to follow rules.

I think a similar issue occurs in gambling, which is like investing, and so people have a rule, intuitively, that risk taking is good. Yet, applied to some domains, such as equities, this rule does not work, as the average individual investor pays too much in transactions, and suffers due to a lack of diversification. Risk taking is good, in general, but not in the stock market. So we see too much gambling.

This is an positive view, an idea about what is, rather than what should be.

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