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Journal of Logic, Language and Information

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04-06-2018

Strategic Conversations Under Imperfect Information: Epistemic Message Exchange Games

Authors: Nicholas Asher, Soumya Paul

Published in: Journal of Logic, Language and Information | Issue 4/2018

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Abstract

This paper refines the game theoretic analysis of conversations in Asher et al. (J Philos Logic 46:355–404, 2017) by adding epistemic concepts to make explicit the intuitive idea that conversationalists typically conceive of conversational strategies in a situation of imperfect information. This ‘epistemic’ turn has important ramifications for linguistic analysis, and we illustrate our approach with a detailed treatment of linguistic examples.

previous article Intertheoretic Reduction, Confirmation, and Montague’s Syntax-Semantics Relation

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It is known that sigma algebras are not sufficient to reason about the information of the players while strategising and can lead to paradoxical results (Dubra and Echenique 2004). Such paradoxes are avoided in our setting because it is the Jury who determines the winning sets \( Win _0, Win _1\) of the players and these sets are not subject to measurability restrictions.

Asher and Lascarides (2003) modelled the inference with a non-monotonic logic, with which we could infer the disjunction of the relations we have depicted above. But it could not do more than that. We assume here a more probabilistic inference relation to model implicatures, and below we will show how these probabilities are dependent on beliefs about interlocutors.

Note that when the Jury is one of the players itself (say Player i), then its types and beliefs are identical to those of i.

A function \(f: A_1\times A_2\times \cdots A_n \rightarrow B\) is independent of the jth component, \(1\le j\le n\), if for all \(a_j, a'_j\in A_j\), \(f(a_1,a_2,\ldots ,a_j,\ldots ,a_n) = f(a_1,a_2,\ldots ,a'_j,\ldots ,a_n)\).

We choose these two types to illustrate how types can affect interpretation. In reality, there might be many more.

See Asher and Paul (2016b) for a case where an unrestricted conversation might assign players victory conditions with no pair of equilibrium strategies.

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Title: Strategic Conversations Under Imperfect Information: Epistemic Message Exchange Games
Authors: Nicholas Asher
Soumya Paul
Publication date: 04-06-2018
Publisher: Springer Netherlands
Published in: Journal of Logic, Language and Information / Issue 4/2018
Print ISSN: 0925-8531
Electronic ISSN: 1572-9583
DOI: https://doi.org/10.1007/s10849-018-9271-9

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