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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/8411

Title: The inductive and modal proof theory of Aumann's theorem on rationality
Authors: Vestergaard, Rene
Lescanne, Pierre
Ono, Hiroakira
Issue Date: 2006-07-07
Publisher: 北陸先端科学技術大学院大学情報科学研究科
Magazine name: Research report (School of Information Science, Japan Advanced Institute of Science and Technology)
Volume: IS-RR-2006-009
Start page: 1
End page: 17
Abstract: Aumann's Theorem on Rationality is a well-know but also contentious result in economics. It pertains to sequential game theory and says that "common knowledge of rationality leads to backwards-induction equilibria". We present a formalist analysis of the result in a meta-theory with primitive support for proof and definition by induction. The analysis shows in part that validity of the result can be reduced to a so-called modal axiom T. Complementing the particular axiom T of Aumann's set-up, we propose an alternative axiom that results in "decidable (local) rationality leads to backwards-induction equilibria". Aumann's result follows from ours but not vice versa and the two axioms T appear to be independent. Our development has been verified in full detail and fully transparently in the Coq proof assistant. The first part of the article is written as a brief overview of the theory behind formal, inductive, and proof-theoretic reasoning in a mechanised proof assistant, such as Coq. It is our contention that such tools go well with sequential game theory and we advocate more wide-spread usage.
URI: http://hdl.handle.net/10119/8411
Material Type: publisher
Appears in Collections:IS-RR-2006

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