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Research Report - School of Information Science ： ISSN 0918-7553 >
IS-RR-2006 >
Please use this identifier to cite or link to this item:
https://hdl.handle.net/10119/8411
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| 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: | https://hdl.handle.net/10119/8411 |
| Material Type: | publisher |
| Appears in Collections: | IS-RR-2006
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Size | Format |
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| IS-RR-2006-009.pdf | | 1267Kb | Adobe PDF | View/Open |
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