On the Impossibility of Predicting the Behavior of Rational Agents

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 players?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 in almost every time period someone predicts that his opponent has a non-negligible probability of choosing one action when in fact the opponent is certain to choose a different action We conclude that there are strategic situations where 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