Book contents
- Frontmatter
- Contents
- List of figures
- List of tables
- Acknowledgments
- 1 Introduction
- Part I Standard beliefs in static games
- 2 Belief in the opponents' rationality
- 3 Common belief in rationality
- 4 Simple belief hierarchies
- Part II Lexicographic beliefs in static games
- Part III Conditional beliefs in dynamic games
- Bibliography
- Index
3 - Common belief in rationality
Published online by Cambridge University Press: 05 July 2012
- Frontmatter
- Contents
- List of figures
- List of tables
- Acknowledgments
- 1 Introduction
- Part I Standard beliefs in static games
- 2 Belief in the opponents' rationality
- 3 Common belief in rationality
- 4 Simple belief hierarchies
- Part II Lexicographic beliefs in static games
- Part III Conditional beliefs in dynamic games
- Bibliography
- Index
Summary
Beliefs about the opponents' beliefs
The main message from the previous chapter is that choosing wisely is more than just choosing rationally: A reasonable choice should not only be rational, in the sense that it can be supported by some belief about the opponents' choices, but it should be optimal for a reasonable belief about the opponents. The main question we will ask ourselves in this book is: When can a belief about the opponents be called reasonable?
The previous chapter was only a first step towards answering this question. In the second half of that chapter we concentrated on beliefs that only assign positive probability to the opponents' choices that are rational for them. Such beliefs are said to express “belief in the opponents' rationality.” This is not the end of the story, however, since not every belief that expresses belief in the opponents' rationality will be entirely reasonable. As an illustration of this fact let us return to the example “Where to locate my pub?”
Example 3.1 Where to locate my pub?
Recall the story from Example 2.1. In Example 2.5 we saw that, if you believe that Barbara chooses rationally, then you can rationally choose the locations c, d and e yourself. The easiest way to see this is to look at the beliefs diagram in Figure 3.1, which is taken from the previous chapter. You can rationally choose c if you believe that Barbara rationally chooses b. Moreover, you can rationally choose d if you believe that Barbara rationally chooses d as well.
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- Information
- Epistemic Game TheoryReasoning and Choice, pp. 68 - 133Publisher: Cambridge University PressPrint publication year: 2012