PP-2006-33: Löwe, Benedikt and Pacuit, Eric (2006) An abstract approach to reasoning about games with mistaken and changing beliefs. [Report]
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Abstract
Both logic and game theory have developed an interest in analyzing
what constitutes rational behaviour under uncertainty. One particular
interesting encounter between logic and game theory is the use of
belief revision techniques as a means of analysis of games.
The game-theoretic analysis of rationality and the study of belief
revision have in common that they have a normative hue; they are
(overly) concerned with questions of what constitutes rational
behaviour and what would be quality measures for rationality. On the
purely logical side, without taking into account context, this is a
doomed enterprise: if you believe $p$ and $p \implies q$, and learn
for a fact that $\not q$ holds, then whether you give up $p$ or the
implication will depend on what these statements are and what the
context is.
In this paper, we present an approach to belief revision in games that
renounces any claims of normativity. We shall present an account of
analysis of games in which all agents have beliefs about the
preferences of the other agents and beliefs about those beliefs, and
so on. Based on that happens in the game, they can change their
beliefs, and again, these changes can be the subject of beliefs of the
agents. Our account is purely formal and does not presuppose any
theory of rationality or of belief change. As a consequence, our
account is able to properly describe also bizarre and irrational
behavioiur.
| Item Type: | Report |
|---|---|
| Report Nr: | PP-2006-33 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2006 |
| Uncontrolled Keywords: | belief revision; backward induction; formal languages; games |
| Subjects: | Language |
| Depositing User: | Benedikt |
| Date Deposited: | 12 Oct 2016 14:36 |
| Last Modified: | 12 Oct 2016 14:36 |
| URI: | https://eprints.illc.uva.nl/id/eprint/208 |
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