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Common Knowledge, Coherent Uncertainties and Consensus

Professor Yakov Ben-Haim
Faculty of Mechanical Engineering, Technion - Israel Institute of Technology
Email: yakov@aluf.technion.ac.il|

Date: 5 March 2002
Time: 1:00pm - 2:30pm
Venue: CARR Seminar Room, H615
Common Knowledge, Coherent Uncertainties and Consensus

Abstract

In conflicts or games, "common knowledge" refers to what one protagonist knows about another protagonist's knowledge. Common knowledge carries special strategic significance.

Examples

SEARCH AND EVASION: If Bin Laden knows that the Americans know where Bin Laden is hiding, then this will significantly influence Bin Laden's behaviour.

TEAMWORK: Collaboration requires information transfer, but this is costly. It is desirable to transfer just enough information for the recipient to perform his task, and for the sender to know that the recipient is triggered to act.

CONSENSUS: When can people DISAGREE about the facts and yet still AGREE about what to do?
In this talk we formulate common knowledge in the context of info-gap decision theory. We discuss three THEOREMS, whose meanings are:

  1. Knowledge is constricted as info-gap uncertainty grows.

  2. Complete common knowledge is possible only without uncertainty. Common knowledge trades off against uncertainty. This entails a temporal implication: limitation on foresight.

  3. Consensus is possible even if the parties have different knowledge. The limitation on the divergence of knowledge which does not jeopardize is expressed by the info-gap coherence functions.
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