Book in progress

Epistemic Game Theory II: Non-Standard Games

In March 2018, I started working on a new textbook called "Epistemic Game Theory II: Non-Standard Games".

It will be a follow-up to my book called "Epistemic Game Theory: Reasoning and Choice". The purpose of the new book will be to explore non-standard games, such as games with incomplete information, games with unawareness and psychological games, in a unified way from an epistemic perspective.

In games with incomplete information the players may have uncertainty about the opponents' utility functions. In games with unawareness the players may be unaware of some choices for the opponents, or even some of the choices for themselves. In psychological games, the utility of a player may not only depend on his choice and and his first-order belief about the opponents' choices, but also on what he believes about the opponents' beliefs.

Despite the difference between these various classes of games, this book will show that these games can be explored in a unified way from an epistemic perspective. For each of these game classes, we will investigate the central concept of common belief in rationality and an associated recursive procedure, together with some version of Nash equilibrium and correlated equilibrium. For dynamic games, we will focus, for each of these classes of games, on the backward induction concept of common belief in future rationality and the forward induction concept of common strong belief in rationality.

 

In the book we will start, however, with standard games as a reference point. Chapter 2 of the book, on common belief in rationality in standard games, is now ready. The chapter can be downloaded below.

 

Part 1: Standard Static Games

 

Chapter 2: Common Belief in Rationality

2.1 Idea of common belief in rationality

2.2 Games and decision problems

2.3 Belief hierarchies, beliefs diagrams and types

2.4 Definition of common belief in rationality

2.5 Recursive procedure

2.6 Why the procedure works

2.7 Order of elimination

2.8 Proofs

Solutions to in-chapter questions

Problems

Literature

 

Bibliography