6 - Correct and Symmetric Beliefs with Incomplete Information

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 generalized 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 Bayesian equilibrium. It subsequently investigates the one theory per choice-utility pair condition, and demonstrates how it leads to canonical Bayesian equilibrium when combined with common belief in rationality and a symmetric belief hierarchy. The chapter finally turns to the scenario of fixed beliefs on utilities, where the players hold some pre-specified beliefs about the opponents’ utility functions.