Interactive and Common Knowledge in the State-Space Model

CESMEP WP Series 03/2009 U. of Torino Department of Economics

23 Pages Posted: 19 Mar 2009 Last revised: 21 May 2011

See all articles by Ivan Moscati

Ivan Moscati

University of Insubria - Department of Economics; Bocconi University - Baffi Carefin Centre; London School of Economics & Political Science (LSE) - Centre for Philosophy of Natural and Social Science (CPNSS)

Date Written: March 18, 2009

Abstract

This paper deals with the prevailing formal model for knowledge in contemporary economics, namely the state-space model introduced by Robert Aumann in 1976. In particular, the paper addresses the following question arising in this formalism: in order to state that an event is interactively or commonly known among a group of agents, do we need to assume that each of them knows how the information is imparted to the others? Aumann answered in the negative, but his arguments apply only to canonical, i.e., completely specified state spaces, while in most applications the state space is not canonical. This paper addresses the same question along original lines, demonstrating that the answer is negative for both canonical and not-canonical state spaces. Further, it shows that this result ensues from two counterintuitive properties held by knowledge in the state-space model, namely Substitutivity and Monotonicity.

Keywords: Interactive knowledge, Common knowledge, State-space model, Substitutivity, Monotonicity

JEL Classification: B40, C70, D80, D82, D83

Suggested Citation

Moscati, Ivan, Interactive and Common Knowledge in the State-Space Model (March 18, 2009). CESMEP WP Series 03/2009 U. of Torino Department of Economics, Available at SSRN: https://ssrn.com/abstract=1362605 or http://dx.doi.org/10.2139/ssrn.1362605

Ivan Moscati (Contact Author)

University of Insubria - Department of Economics ( email )

Via Monte Generoso 71
Varese, 21100
Italy

Bocconi University - Baffi Carefin Centre ( email )

Via Roentgen 1
Milan
Italy

London School of Economics & Political Science (LSE) - Centre for Philosophy of Natural and Social Science (CPNSS) ( email )

London
United Kingdom

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