PP-2006-33: An abstract approach to reasoning about games with mistaken and changing beliefs

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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