On the impossibility of predicting the behavior of rational agents

From: J. R. Molloy (jr@shasta.com)
Date: Thu Oct 25 2001 - 16:54:27 MDT

Edited by Richard D. McKelvey, California Institute of Technology, Pasadena,
CA, and approved August 1, 2001 (received for review November 8, 2000)
A foundational assumption in economics is that people are rational: they
choose optimal plans of action given their predictions about future states of
the world. In games of strategy this means that each player's strategy should
be optimal given his or her prediction of the opponents' strategies. We
demonstrate that there is an inherent tension between rationality and
prediction when players are uncertain about their opponents' payoff functions.
Specifically, there are games in which it is impossible for perfectly rational
players to learn to predict the future behavior of their opponents (even
approximately) no matter what learning rule they use. The reason is that in
trying to predict the next-period behavior of an opponent, a rational player
must take an action this period that the opponent can observe. This
observation may cause the opponent to alter his next-period behavior, thus
invalidating the first player's prediction. The resulting feedback loop has
the property that, a positive fraction of the time, the predicted probability
of some action next period differs substantially from the actual probability
with which the action is going to occur. We conclude that there are strategic
situations in which it is impossible in principle for perfectly rational
agents to learn to predict the future behavior of other perfectly rational
agents based solely on their observed actions.

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Useless hypotheses, etc.:
 consciousness, phlogiston, philosophy, vitalism, mind, free will, qualia,
analog computing, cultural relativism, GAC, Cyc, Eliza, cryonics, individual
uniqueness, ego, human values, scientific relinquishment

We move into a better future in proportion as science displaces superstition.

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