Belief revision

In the first two parts of this book we considered so-called static games. These are situations where every player only makes one choice, and at the time of his choice a player does not have any information about the choices of his opponents. It may be, for instance, that all players decide simultaneously and independently. Another possibility is that the players choose at different points in time, but that they have not learnt anything about past choices of the opponents when it is their time to choose. In such situations there is no need to change your belief during a game, as you do not receive any information about your opponents up to the moment when you must make your choice. We can therefore model a player's belief in a static game by a single, static belief hierarchy, which does not change over time.

In this part of the book we will study dynamic games, which are situations where a player may have to make several choices over a period of time, and where he may learn about the opponents' previous choices during the game. This will cover a much broader spectrum of situations than static games, but the analysis will also be a bit harder here. The main reason is that a player in a dynamic game may have to revise his beliefs about the opponents during the game, as he may observe choices by the opponents that he did not expect before the game started. So it will no longer be sufficient to model a player's beliefs by a single, static belief hierarchy.