Journal of Philosophical Logic

, Volume 46, Issue 4, pp 355–404 | Cite as

Message Exchange Games in Strategic Contexts

  • Nicholas AsherEmail author
  • Soumya Paul
  • Antoine Venant


When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call such games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions (decomposition invariant winning conditions) for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically.


Philosophy of language Dialogue Game theory Strategic reasoning 


  1. 1.
    Asher, N., & Lascarides, A. (2003). Logics of conversation: Cambridge University Press.Google Scholar
  2. 2.
    Asher, N., & Lascarides, A. (2013). Strategic conversation. Semantics and Pragmatics, 6.2, 1–62.Google Scholar
  3. 3.
    Asher, N., Paul, S., & Venant, A. (2015). Conversational goals and achieving them in no-win situations: Submitted to Journal of Logic Language and Information.Google Scholar
  4. 4.
    Asher, N., & Paul, S. (2016) In J. Hunter , M. Stone, & M. Simons (Eds.), Evaluating conversational success: Weighted Message Exchange Games. New Brunswick, New Jersey, USA: Semdial.Google Scholar
  5. 5.
    Aumann, R.J., & Hart, S. (2003). Long cheap talk. Econometrica, 71(6), 1619–1660.CrossRefGoogle Scholar
  6. 6.
    Aumann, R.J., & Maschler, M. (1995). Repeated games with incomplete information: MIT Press.Google Scholar
  7. 7.
    Axelrod, R.M. (2006). The evolution of cooperation: Basic Books.Google Scholar
  8. 8.
    Benz, A. Jäger, G., & Van Rooij, R. (Eds.) (2005). Game theory and pragmatics: Palgrave Macmillan.Google Scholar
  9. 9.
    Büch, J.R., & Landweber, L.H. (1969). Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, 138, 367–378.Google Scholar
  10. 10.
    Chang, C.C., & Keisler, H.J. (1973). Model theory north: Holland Publishing.Google Scholar
  11. 11.
    Chaterjee, K. (2007). Concurrent games with tail objectives. Theoretical Computer Science, 388, 181–198.CrossRefGoogle Scholar
  12. 12.
    Crawford, V., & Sobel, J. (1982). Strategic information transmission. Econometrica, 50(6), 1431–1451.CrossRefGoogle Scholar
  13. 13.
    Dung, P.M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial intelligence, 77(2), 321–357.CrossRefGoogle Scholar
  14. 14.
    Farrell, J. (1993). Meaning and credibility in cheap-talk games. Games and Economic Behaviour, 5, 514–531.CrossRefGoogle Scholar
  15. 15.
    Franke, M. (2008). Meaning and inference in case of conflict. In Balogh, K. (Ed.) Proceedings of the 13th ESSLLI Student Session (pp. 65–74).Google Scholar
  16. 16.
    Franke, M. (2009). Signal to Act: Game Theory in Pragmatics. ILLC dissertation series. Institute for Logic, Language and Computation.Google Scholar
  17. 17.
    Franke, M., De Jager, T., & Rooij, R. (2009). Relevance in cooperation and conflict. Journal of Logic and Language.Google Scholar
  18. 18.
    Glazer, J., & Rubinstein, A. (2001). Debates and decisions: on a rationale of argumentation rules. Games and Economic Behavior, 36(2), 158–173.CrossRefGoogle Scholar
  19. 19.
    Glazer, J., & Rubinstein, A. (2004). On optimal rules of persuasion. Econometrica, 72(6), 119–123.CrossRefGoogle Scholar
  20. 20.
    Grädel, E. (2008). Banach-Mazur games on graphs. In Hariharan, R., Mukund, M., & Vinay, V. (Eds.) Foundations of Software Technology and Theoretical Computer Science (FSTTCS) (pp. 364–382).Google Scholar
  21. 21.
    Grice, H.P. (1975). Logic and conversation. In Cole, P., & Morgan, J.L. (Eds.) Syntax and Semantics Volume 3: Speech Acts (pp. 41–58): Academic Press.Google Scholar
  22. 22.
    Grosz, B., & Sidner, C. (1986). Attention, intentions and the structure of discourse. Computational Linguistics, 12, 175–204.Google Scholar
  23. 23.
    Grosz, B.J., & Kraus, S. (1993). Collaborative plans for group activities. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (pp. 367–373). Los altos, California: Morgan Kaufmann.Google Scholar
  24. 24.
    Kechris, A. (1995). Classical descriptive set theory. New York: Springer-Verlag.Google Scholar
  25. 25.
    Lamport, L. (1980). Sometime is sometimes not never: On the temporal logic of programs. In Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (pp. 174–185): ACM.Google Scholar
  26. 26.
    Lewis, D. (1969). Convention: A philosophical study, Harvard University Press.Google Scholar
  27. 27.
    Libkin, L. (2004). Elements of finite model theory: Springer.Google Scholar
  28. 28.
    Malone, P. (2009). The life you save: Nine Steps to Finding the Best Medical Care and Avoiding the Worst: Da Capo Lifelong.Google Scholar
  29. 29.
    Mann, W.C., & Thompson, S.A. (1987). Rhetorical structure theory: A framework for the analysis of texts. International Pragmatics Association Papers in Pragmatics, 1, 79–105.Google Scholar
  30. 30.
    Martin, D.A. (1975). Borel determinacy. Annals of Mathematics, 102(2), 363–371.CrossRefGoogle Scholar
  31. 31.
    Mauldin, R. (Ed.) (1981). The Scottish Book. Mathematics from the Scottish Café: Birkhaüser.Google Scholar
  32. 32.
    McNaughton, R., & Papert, S. (1971). Counter-free automata. In Research Monograph, Vol. 65: MIT Press.Google Scholar
  33. 33.
    Oxtoby, J. (1957). The Banach-Mazur game and Banach category theorem. Contribution to the Theory of Games, 3, 159–163.Google Scholar
  34. 34.
    Parikh, P. (1991). Communication and strategic inference. Linguistics and Philosophy, 14(5), 473–514.CrossRefGoogle Scholar
  35. 35.
    Parikh, P. (2000). Communication, meaning and interpretation. Linguistics and Philosophy, 25, 185–212.CrossRefGoogle Scholar
  36. 36.
    Parikh, P. (2001). The use of language. Stanford, California: CSLI Publications.Google Scholar
  37. 37.
    Perrin, D., & Pin, J.E. (2004). Infinite Words: Automata, Semigroups, Logic and Games: Elsevier Publications.Google Scholar
  38. 38.
    Rabin, M. (1990). Communication between rational agents. Journal of Economic Theory, 51, 144–170.CrossRefGoogle Scholar
  39. 39.
    Revalski, J.P.. The Banach-Mazur game: history and recent developments. Technical report, Institute of Mathematics and Informatics, (pp. 2003–2004): Bulgarian Academy of Sciences.Google Scholar
  40. 40.
    Sacks, H. Lectures on Conversation. Blackwell Publishers, Oxford, 1992. Edited by Gail Jefferson. This is the published version of lecture notes from 1967–1972.Google Scholar
  41. 41.
    Solan, L.M., & Tiersma, P.M. (2005). Speaking of Crime: The language of criminal justice. Chicago, IL: University of Chicago Press.Google Scholar
  42. 42.
    Spence, A.M. (1973). Job market signaling. Journal of Economics, 87(3), 355–374.Google Scholar
  43. 43.
    Traum, D., & Allen, J. (1994). Discourse obligations in dialogue processing. In Proceedings of the 32nd Annual Meeting of the Association for Computational Linguistics (ACL94) (pp. 1–8). Las Cruces New, Mexico.Google Scholar
  44. 44.
    Van Rooij, R. (2003). Being polite is a handicap: towards a game theoretical analysis of polite linguistic behavior. In TARK (pp. 45–58).Google Scholar
  45. 45.
    van Rooij, R. (2004). Signalling games select horn strategies. Linguistics and Philosophy, 27, 493–527.CrossRefGoogle Scholar
  46. 46.
    Venant, A., & Asher, N. (2015). Ok or not ok? commitments, acknowledgments and corrections. In Proceedings of Semantics and Linguistic Theory (SALT 25). Stanford.Google Scholar
  47. 47.
    Venant, A., Asher, N., & Dégremont, C. (2014). Credibility and its attacks. In Proceedings of Semdial 2014. Semdial.Google Scholar
  48. 48.
    Walton, D.N. (1984). Logical dialogue-gamES. Lanham, Maryland: University Press of America.Google Scholar
  49. 49.
    Zwick, U., & Paterson, M.S. (1995). The complexity of mean payoff games. In Computing and Combinatorics (pp. 1–10): Springer.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.CNRSIRITToulouseFrance
  2. 2.Université de Toulouse 3, IRITToulouseFrance

Personalised recommendations