4 - Correct and Symmetric Beliefs in Standard Games

Summary

This chapter starts by introducing the notion of a simple belief hierarchy, and shows that a simple belief hierarchy in combination with common belief in rationality leads to Nash equilibrium. It then turns to the weaker notion of symmetric belief hierarchies and shows, in a similar fashion, that a symmetric belief hierarchy in combination with common belief in rationality leads to correlated equilibrium. It finally investigates the one theory per choice condition, and demonstrates how it leads to canonical correlated equilibrium when combined with common belief in rationality and a symmetric belief hierarchy.