On the Impossibility of Predicting the Behavior of Rational Agents
H. Peyton Young, Dean P. Foster · 2024
Abstract 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 a game this means that each player’s strategy should be optimal given his or her prediction about the opponents’ strategies. This chapter demonstrates that there are games in which it is impossible for perfectly rational players to learn to predict the future behavior of their opponents. The reason is that, in trying to predict the next-period behavior of the opponent, a rational player will take an action this period that the opponent can observe. This observation may cause the opponent to alter his next-period behavior, which can invalidate the first player’s prediction. The resulting feedback loop has the property that, a positive fraction of the time, the predicted probability of an opponent’s action will differ from its actual probability. Thus there are games in which it is impossible in principle for perfectly rational agents to learn to predict the behavior of their perfectly rational opponents based solely on their observed actions.