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Strategic Conversations Under Imperfect Information: Epistemic Message Exchange Games

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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.

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Notes

  1. 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.

  2. 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.

  3. 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.

  4. 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 \(a_j, a'_j\in A_j\), \(f(a_1,a_2,\ldots ,a_j,\ldots ,a_n) = f(a_1,a_2,\ldots ,a'_j,\ldots ,a_n)\).

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

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

References

  • Afantenos, S., Kow, E., Asher, N., & Perret, J. (2015). Discourse parsing for multi-party chat dialogues. In Proceedings of the 2015 conference on empirical methods in natural language processing (pp. 928–937). Lisbon, Portugal: Association for Computational Linguistics.

  • Asher, N., & Lascarides, A. (2003). Logics of conversation. Cambridge: Cambridge University Press.

    Google Scholar 

  • Asher, N., & Lascarides, A. (2009). Agreement, disputes and commitment in dialogue. Journal of Semantics, 26(2), 109–158.

    Article  Google Scholar 

  • Asher, N., & Lascarides, A. (2013). Strategic conversation. Semantics and Pragmatics, 6(2), 1–62.

    Google Scholar 

  • Asher, N., & Paul, S. (2016a). Evaluating conversational success: Weighted message exchange games. In J. Hunter, M. Simons, & M. Stone (Eds.), 20th Workshop on the semantics and pragmatics of dialogue (SEMDIAL) (pp. 55–64). New Jersey, USA.

  • Asher, N., & Paul, S. (2016b). Language games. In Proceedings of the 20th international conference on logical aspects of computational linguistics (LACL) (pp. 1–17). Berlin: Springer.

    Google Scholar 

  • Asher, N., & Paul, S. (2016c). Strategic reasoning in conversations under imperfect information. In Z. Sikić et al. (Eds.), Proceedings of the 5th conference on logic and applications (LAP). Dubrovnik: IUC.

  • Asher, N., Paul, S., & Venant, A. (2017). Message exchange games in strategic contexts. Journal of Philosophical Logic, 4(4), 355–404.

    Article  Google Scholar 

  • Aumann, R. (1961). Borel structures for function spaces. Illinois Journal of Mathematics, 5, 614–630.

    Google Scholar 

  • Aumann, R. J. (1976). Agreeing to disagree. The Annals of Statistics, 4(6), 1236–1239.

    Article  Google Scholar 

  • Banks, J. S., & Sundaram, R. K. (1994). Switching costs and the Gittins index. Econometrica: Journal of the Econometric Society, 62(3), 687–694.

    Article  Google Scholar 

  • Benz, A. (2012). Errors in pragmatics. Journal of Logic, Language and Information, 21(1), 97–116.

    Article  Google Scholar 

  • Bubeck, S., & Cesa-Bianchi, N. (2012). Regret analysis of stochastic and nonstochastic multi-armed bandit problems. Foundations and Trends \(^{\textregistered }\) Machine Learning, 5(1), 1–122.

    Article  Google Scholar 

  • Cesa-Bianchi, N., & Lugosi, G. (2006). Prediction, learning, and games. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Dekel, E., & Siniscalchi, M. (2015). Epistemic game theory. Handbook of Game Theory with Economic Applications, 4(1), 609–702.

    Google Scholar 

  • Dubra, J., & Echenique, F. (2004). Information is not about measurability. Mathematical Social Sciences, 47(2), 177–185.

    Article  Google Scholar 

  • Franke, M. (2008). Meaning and inference in case of conflict. In K. Balogh (Ed.), Proceedings of the 13th ESSLLI student session (pp. 65–74).

  • Harsanyi, J. C. (1967). Games with incomplete information played by Bayesian players, parts i–iii. Management Science, 14, 159–182.

    Article  Google Scholar 

  • Pacuit, E., & Roy, O. (2015). Epistemic foundations of game theory. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy.

  • Parikh, P. (2001). The use of language. Stanford, CA: CSLI Publications.

    Google Scholar 

  • Parikh, P. (2010). Language and equilibrium. Cambridge, MA: MIT Press.

    Book  Google Scholar 

  • Perrin, D., & Pin, J. E. (1995). Infinite words—Automata, semigroups, logic and games. New York: Elsevier.

    Google Scholar 

  • Solan, L. M., & Tiersma, P. M. (2005). Speaking of crime: The language of criminal justice. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Stevens, J. S., Benz, A., Reuße, S., & Klabunde, R. (2016). Pragmatic question answering: A game-theoretic approach. Data & Knowledge Engineering, 106, 52–69.

    Article  Google Scholar 

  • van Rooij, R. (2004). Signalling games select horn strategies. Linguistics and Philosophy, 27, 493–527.

    Article  Google Scholar 

  • Venant, A., Asher, N., & Degremont, C. (2014). Credibility and its attacks. In V. Rieser & P. Muller (Eds.), The 18th workshop on the semantics and pragmatics of dialogue (pp. 154–162).

  • Whittle, P. (1980). Multi-armed bandits and the Gittins index. Journal of the Royal Statistical Society. Series B (Methodological), 42(2), 143–149.

    Google Scholar 

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Author information

Authors and Affiliations

  1. IRIT, CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France

    Nicholas Asher

  2. SnT, Université du Luxembourg, 6 avenue de la Fonte, L-4364, Esch-sur-Alzette, Luxembourg

    Soumya Paul

Authors
  1. Nicholas Asher
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  2. Soumya Paul
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Correspondence to Soumya Paul.

Additional information

Thanks to Julie Hunter, Alex Lascarides, David Beaver, Eric McCready, Daisuke Bekki, Chris Barker, Erich Grädel, Hans Kamp, Benedikt Löwe, Julian Schlöder, Itai Sher, to the participants of the Rutgers Workshop on Coordination and Content and to reviewers for the Journal of Logic, Language and Information for their helpful comments on previous versions of this paper. This work was supported by ERC Grant 269427.

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Asher, N., Paul, S. Strategic Conversations Under Imperfect Information: Epistemic Message Exchange Games. J of Log Lang and Inf 27, 343–385 (2018). https://doi.org/10.1007/s10849-018-9271-9

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  • DOI: https://doi.org/10.1007/s10849-018-9271-9

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