# What is the difference between a perfect foresight equilibrium and a rational expections equilibrium?

What is the difference between a perfect foresight equilibrium and a rational expections equilibrium?

Why is it the same in case of a non-stochastic model?

Can there be a perfect foresight equilibrium in a stochastic model?

• This is a great question, but to be sure I can speak exactly to your point, do you mind sharing the source where you saw the definition of PFE, and REE as well as the statement that these solution concepts coincide when the model is non-stochastic. Apr 19, 2020 at 23:21
• Thanks. I read these statements in Evans and Honkapohja (2001), expectations and learning in macroeconimcs, I think. They use these terms without really explaining them. Check the following google books link : books.google.be/… Apr 24, 2020 at 16:02
• That makes sense these concepts can take various forms depending on the type of model you are working on, so probably that is why they decided to treat the concepts less formally. I will attempt an answer to your question. Apr 24, 2020 at 17:10

This is not a formal definition, but a useful piece of intuition. I think that the best way to think about it is that when there is uncertainty in a model it arises mainly in two forms either there is information that some agents have, but not every agent has it (private information), or there are truly random events that no one knows (in game theory jargon, these are moves by nature).

This difference is key because private information affects agents' decisions. So for example, if the model predicts that people will act differently depending on their private information, a rational expectation equilibrium assumes that everyone understands this, and so by observing people's actions, they can infer their private information. If the "relevant outcome" that agents have to predict. depends only on all the private information dispersed among people, probably you can see how you can get people behaving as if they had perfect foresight.

Contrast the assumption of rational expectations with an assuming that agents are agnostic about how other agents use their private information to make decisions, or with assuming that agents predict the "relevant outcome" only using their own private information and past trends of the relevant outcome. In these cases, we should not expect a perfect foresight equilibrium.

How does that relate to stochastic models?

If the source of uncertainty is not only the existence of private information, but also "true randomness" then even a rational expectations equilibrium will not have perfect foresight (except perhaps by coincidence). Loosely speaking, if the model is stochastic, then it will predict many possible outcomes (each with some probability attached, perhaps), and agents will also expect these outcomes in a rational expectations equilibrium. Thus maybe agents make a decision based on the most likely outcome, however, this outcome may or may not occur (i.e. no perfect foresight).