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.

Chapter 8 delves into the complexities introduced by asymmetric information, where some contestants possess more information than others, or neither of the contestants has complete information about the characteristics of the others. The chapter examines contests in which the true common value of the prize may be unknown to certain contestants, such as an incumbent having a better understanding of the value of office than a challenger, or a current resource owner having more information about its true value than potential entrants. It also examines situations where no contestant has complete information about the value assigned for each contestant to the prize, such as companies competing to develop a new product or technology. Each company knows its own valuation of the potential market but does not know the competitor’s valuation. The chapter also analyzes the existence and properties of equilibrium and other related questions, such as the following: How do outcomes in complete and incomplete information scenarios compare? Should a well-informed planner disclose information to maximize total effort in a contest involving both informed and uninformed contestants?