Ambiguous Language and Consensus∗

Standard economic models cannot capture the fact that information is often ambiguous, and is interpreted in multiple ways. Using a framework that distinguishes between the language in which statements are made and the interpretation of statements, we show that ambiguity can have important consequences. We show that players can agree to disagree in the presence of ambiguity, even if there is a common prior, but that allowing for ambiguity is more restrictive than assuming heterogeneous priors. We also demonstrate that, unlike in the case where there is no ambiguity, players may come to have different beliefs starting from a common prior, even if they have received exactly the same information, unless the information is common knowledge. Taken together, these results suggest that ambiguity provides a potential explanation for heterogeneous beliefs. At the same time, it imposes nontrivial restrictions on the situations that can be modeled, so that it is not the case that “anything goes” once we allow for ambiguous statements. ∗A preliminary version of this work appeared as “Ambiguous language and differences in beliefs” in the Principles of Knowledge Representation and Reasoning: Prceedings of the Thirteenth International Conference, 2012, pp. 329–338. We thank Moshe Vardi for helpful comments. Halpern’s work was supported in part by NSF grants IIS-0534064, IIS-0812045, IIS-0911036, and CCF-1214844, by AFOSR grants FA9550-08-1-0438, FA9550-12-1-0040, and FA9550-09-1-0266, and by ARO grant W911NF-09-10281. The work of Kets was supported in part by AFOSR grant FA9550-08-1-0389. †Computer Science Dept., Cornell University, Ithaca, NY. E-mail: [email protected]. ‡Kellogg School of Management, Northwestern University, Evanston, IL. E-mail: [email protected].