Strong Belief and Forward Induction Reasoning

Battigalli, Pierpaolo; Siniscalchi, Marciano

doi:10.1006/jeth.2001.2942

Cited by 277 publications

(331 citation statements)

References 26 publications

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“…This notion is called "strong belief" by Battigalli and Siniscalchi [13], while Stalnaker [50] calls it "robust belief". Another characterization of strong belief is the following s |= SbaQ iff: s |= BaQ and s |= B P a Q for every P such that s |= ¬Ka(P → ¬Q)…”

Section: But a More Useful Characterization Is The Followingmentioning

confidence: 99%

A Qualitative Theory of Dynamic Interactive Belief Revision

Baltag

Smets

2016

Readings in Formal Epistemology

177

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We present a logical setting that incorporates a belief-revision mechanism within Dynamic-Epistemic logic. As the "static" basis for belief revision, we use epistemic plausibility models, together with a modal language based on two epistemic operators: a "knowledge" modality K (the standard S5, fully introspective, notion), and a "safe belief" modality 2 ("weak", non-negatively-introspective, notion, capturing a version of Lehrer's "indefeasible knowledge"). To deal with "dynamic" belief revision, we introduce action plausibility models, representing various types of "doxastic events". Action models "act" on state models via a modified update product operation: the "ActionPriority" Update. This is the natural dynamic generalization of AGM revision, giving priority to the incoming information (i.e. to "actions") over prior beliefs. We completely axiomatize this logic, and show how our update mechanism can "simulate", in a uniform manner, many different belief-revision policies.

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Section: But a More Useful Characterization Is The Followingmentioning

confidence: 99%

A Qualitative Theory of Dynamic Interactive Belief Revision

Baltag

Smets

2016

Readings in Formal Epistemology

177

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“…The difference becomes more apparent if we consider the assumption that "rationality" is common belief, in the strongest possible sense, including common "strong" belief (in the sense of Battigalli and Siniscalchi 2002), common persistent belief, or even common "knowledge" in the sense of Aumann. As correctly argued by Stalnaker and Reny, these assumptions, if applied to the usual notions of rationality in the literature, bear no relevance for what the players would do (or believe) at the nodes that are incompatible with these assumptions!…”

Section: Solving the Bi Paradoxmentioning

confidence: 99%

“…The work of Battigalli and Siniscalchi (2002) is the closest to ours, both through their choice of the basic setting for the "static logic" (also given by conditional belief operators) and through the introduction of a strengthened form of common belief ("common strong belief") as an epistemic basis for a backward-induction theorem. Strong belief, though different from our "stable" belief, is another version of persistent belief: belief that continues to be maintained unless and until it is contradicted by new information.…”

Section: Comparison With Other Workmentioning

confidence: 99%

Keep ‘hoping’ for rationality: a solution to the backward induction paradox

2009

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We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we "simulate" the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of "stable belief", i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann's and compatible with the implicit assumptions (the "epistemic openness of the future") underlying Stalnaker's criticism of Aumann's proof. The "dynamic" nature of our concept of rationality explains why our condition avoids the apparent circularity of the "backward induction paradox": it is consistent to (continue to) believe in a player's rationality after updating with his irrationality.

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“…Higher-order beliefs can also affect economic conclusions in settings ranging from bargaining [2,3] and speculative trade [4] to mechanism design [5] . Higher-order beliefs about actions are central to epistemic characterizations, for example, of rationalizability [6,7], Nash equilibrium [8,9] and forward induction reasoning [10]. In principle, higher-order beliefs can be modeled explicitly, using belief hierarchies.…”

Section: Introductionmentioning

confidence: 99%

When Do Types Induce the Same Belief Hierarchy?

Perea

Kets

2016

Games

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Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy.

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Strong Belief and Forward Induction Reasoning

Cited by 277 publications

References 26 publications

A Qualitative Theory of Dynamic Interactive Belief Revision

A Qualitative Theory of Dynamic Interactive Belief Revision

Keep ‘hoping’ for rationality: a solution to the backward induction paradox

When Do Types Induce the Same Belief Hierarchy?

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