Communication, common knowledge and consensus

Abstract : The aim of this thesis is to study the implications of common knowledge for consensus, following the seminal work of Aumann [1976]. This thesis is made of six chapters. The first two chapters introduce background material and survey the literature. The three next chapters are original contributions. The last chapter compares various conditions introduced in chapters 3 and 4 with conditions of the literature. In chapter 3, we generalize Aumann's result to the case of common knowledge of a statistic of individual decisions. We show that if decision rules are balanced union consistent, and if the statistic is exhaustive, then common knowledge of the statistic of individual decisions implies that all decisions are the same. In chapter 4, we study what conditions are sufficient to guarantee that communication of individual decisions eventually leads to a consensus on decisions. We show that if the protocol is fair, and if agents communicate the action that maximizes their expected utility, then communication eventually leads to consensus. The starting point of chapter 5 is the observation that different communication protocols may lead to different outcomes, in terms of consensus as well as of the amount of information learned by the agents during the process. We show that if it is common knowledge among a group of agents that some of them disagree about the protocol they should use for communicate, then the consensus value must be the same, whatever the protocol.
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Economies and finances. Université Panthéon-Sorbonne - Paris I, 2006. English
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  • HAL Id : tel-00174147, version 1



Lucie Ménager. Communication, common knowledge and consensus. Economies and finances. Université Panthéon-Sorbonne - Paris I, 2006. English. 〈tel-00174147〉



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