Ambiguous Language and Differences in Beliefs
This addresses a foundational issue in multi-agent systems and economics by revealing how ambiguity affects agreement and belief dynamics, though it is incremental in extending existing logic frameworks.
The paper tackles the problem that standard multi-agent modal logic models fail to account for ambiguous information interpreted differently by agents, proposing a framework to model this and showing that ambiguity invalidates Aumann's result that agents with a common prior cannot agree to disagree.
Standard models of multi-agent modal logic do not capture the fact that information is often ambiguous, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents' beliefs regarding whether or not there is ambiguity. We consider the impact of ambiguity on a seminal result in economics: Aumann's result saying that agents with a common prior cannot agree to disagree. This result is known not to hold if agents do not have a common prior; we show that it also does not hold in the presence of ambiguity. We then consider the tradeoff between assuming a common interpretation (i.e., no ambiguity) and a common prior (i.e., shared initial beliefs).