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Substantive assumptions in interaction: a logical perspective

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Abstract

In this paper we study substantive assumptions in social interaction. By substantive assumptions we mean contingent assumptions about what the players know and believe about each other’s choices and information. We first explain why substantive assumptions are fundamental for the analysis of games and, more generally, social interaction. Then we show that they can be compared formally, and that there exist contexts where no substantive assumptions are being made. Finally we show that the questions raised in this paper are related to a number of issues concerning “large” structures in epistemic game theory.

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References

  • Abramsky, S., & Zvesper, J. A. (2012). From Lawvere to Brandenburger-Keisler: Interactive forms of diagonalization and self-reference. Colagebraic Methods in Computer Science, LNCS, 7399 1–19.

  • Aumann R. J. (1987) Correlated equilibrium as an expression of bayesian rationality. Econometrica 55: 1–18

    Article  Google Scholar 

  • Aumann R. J. (1999) Interactive epistemology I: Knowledge. International Journal of Game Theory 28: 263–300

    Article  Google Scholar 

  • Aumann, R. (2010). Interview on epistemic logic. In Hendricks, V., & Roy, O. (Eds.), Epistemic logic, 5 questions. New York: Automatic Press.

  • Aumann R., Dreze J. (2008) Rational expectations in games. American Economic Review 98: 72–86

    Article  Google Scholar 

  • Bernheim D. (1984) Rationalizable strategic behavior. Econometrica 52: 1007–1028

    Article  Google Scholar 

  • Blackburn P., de Rijke M., Venema Y. (2001) Modal logic. Cambridge University Press, Cambridge

    Google Scholar 

  • Blackburn, P., van Benthem, J., & Wolter, F. (Eds.). (2006). Handbook of modal logic. Amsterdam: Elsevier.

  • Board O. (2002) Knowledge, beliefs and game-theoretic solution concepts. Oxford Review of Economic Policy 18: 433–445

    Article  Google Scholar 

  • Brandenburger, A. (2003). On the existence of a ‘complete’ possibility structure. In Basili, M., Dimitri, N., & Gilboa, I. (Eds.), Cognitive processes and economic behavior (pp. 30–34). London: Routledge.

  • Brandenburger A. (2007) The power of paradox: Some recent developments in interactive epistemology. International Journal of Game Theory 35: 465–492

    Article  Google Scholar 

  • Brandenburger, A., & Dekel, E. (1993). Hierarchies of beliefs and common knowledge. Journal of Economic Theory, 59, 189–198

    Google Scholar 

  • Brandenburger A., Friedenberg A., Keisler H. J. (2008) Admissibility in games. Econometrica 76: 307–352

    Google Scholar 

  • Brandenburger A., Keisler H. J. (2006) An impossibility theorem on beliefs in games. Studia Logica 84(2): 211–240

    Article  Google Scholar 

  • de Bruin, B. (2010). Explaining games: The epistemic programme in game theory. Synthese Library (Vol. 346). New York: Springer.

  • Fagin R., Halpern J. Y. (1987) Belief, awareness, and limited reasoning. Artificial Intelligence 34(1): 39–76

    Article  Google Scholar 

  • Fagin R., Halpern J. (1994) Reasoning about knowledge and probability. Journal of the ACM 41: 340–367

    Article  Google Scholar 

  • Fagin R., Halpern J., Geanakoplos J., Vardi M. (1999) The hierarchical approach to modeling knowledge and common knowledge. International Journal of Game Theory 28(3): 331–365

    Article  Google Scholar 

  • Fagin R., Halpern J. Y., Moses Y., Vardi M. (1995) Reasoning about knowledge. MIT Press, London

    Google Scholar 

  • Friedenberg A. (2010) When do type structures contain all hierarchies of beliefs?. Games and Economic Behavior 68(1): 108–129

    Article  Google Scholar 

  • Friedenberg, A., & Meier, M. (2010). On the relationship between hierarchy and type morphisms. Economic Theory, 1–23. doi:10.1007/s00199-010-0517-2

  • Goldblatt R. (2006) Final coalgebras and the hennessy-milner property. Annals of Pure and Applied Logic 183: 77–93

    Article  Google Scholar 

  • Goldblatt, R. (2008). Deductive systems for coalgebras over measurable spaces. Journal of Logic and Computation Page. doi:10.1093/logcom/exn092

  • Halpern J. Y. (2001) Alternative semantics for unawareness. Games and Economic Behavior 37(2): 321–339

    Article  Google Scholar 

  • Harel D., Kozen D., Tiuryn J. (2000) Dynamic logic. The MIT Press, London

    Google Scholar 

  • Heifetz A. (1999) How canonical is the canonical model? A comment on Aumann’s interactive epistemology. International Journal of Game Theory 28(3): 435–442

    Article  Google Scholar 

  • Heifetz A., Meier M., Schipper B. C. (2006) Interactive unawareness. Journal of Economic Theory 130(1): 78–94

    Article  Google Scholar 

  • Heifetz A., Mongin P. (2001) Probability logic for type spaces. Games and Economic Behavior 35: 31–53

    Article  Google Scholar 

  • Heifetz A., Samet D. (1998a) Knowledge spaces with arbitrarily high rank. Games and Economic Behavior 22(2): 260–273

    Article  Google Scholar 

  • Heifetz A., Samet D. (1998b) Topology-free typology of beliefs. Journal of Economic Theory 82: 324–341

    Article  Google Scholar 

  • Hintikka J. (1962) Knowledge and belief: An introduction to the logic of two notions. ornell University Press, Ithaca, NY

    Google Scholar 

  • Huber, F., & Schmidt-Petri, C. (2009). Degrees of belief. Synthese Library (Vol. 342). New York: Springer.

  • Mariotti T., Meier M., Piccione M. (2005) Hierarchies of beliefs for compact possibility models. Journal of Mathematical Economics 41: 303–324

    Article  Google Scholar 

  • Meier M. (2005) On the nonexistence of universal information structures. Journal of Economic Theory 122(1): 132–139

    Article  Google Scholar 

  • Meier M. (2006) Finitely additive beliefs and universal type spaces. Annals of Probability 34(1): 386–422

    Article  Google Scholar 

  • Meier M. (2008) Universal knowledge-belief structures. Game and Economic Behavior 62: 53–66

    Article  Google Scholar 

  • Mertens J. F., Zamir S. (1985) Formulation of Bayesian analysis for games with incomplete information. International Journal of Game Theory 14(1): 1–29

    Article  Google Scholar 

  • Modica S., Rustichini A. (1994) Awareness and partitional information structures. Theory and Decision 37(1): 107–124

    Article  Google Scholar 

  • Moscati, I. (2009). Interactive and common knowledge in the state-space model. Cesmep working papers. University of Turin. http://econpapers.repec.org/RePEc:uto:cesmep:200903.

  • Parikh, R. (1991). Monotonic and non-monotonic logics of knowledge. Fundamenta Informaticae, XV, 255–274.

  • Pearce D. (1984) Rationalizable strategic behavior and the problem of perfection. Econometrica 52: 1029–1050

    Article  Google Scholar 

  • Pintér M. (2005) Type space on a purely measurable parameter space. Economic Theory 26(1): 129–139

    Article  Google Scholar 

  • Pintér M. (2010) The non-existence of a universal topological type space. Journal of Mathematical Economics 46(2): 223–229

    Article  Google Scholar 

  • Samuelson L. (2004) Modeling knowledge in economic analysis. Journal of Economic Literature 42(2): 367–403

    Article  Google Scholar 

  • Segerberg K. (1994) A model existence theorem in infinitary propositional modal logic. Journal of Philosophical Logic 23(4): 337–367

    Article  Google Scholar 

  • Siniscalchi, M. (2008). Epistemic game theory: Beliefs and types. In Durlauf, S., & Blume, L. (Eds.), The new palgrave dictionary of economics. Basingstoke: Palgrave Macmillan.

  • Stalnaker R. (1999) Extensive and strategic forms: Games and models for games. Research in Economics 53: 293–319

    Article  Google Scholar 

  • van Benthem J. (2010) Modal logic for open minds. CSLI Publications, Stanford

    Google Scholar 

  • van Benthem J., Girard P., Roy O. (2009) Everything else being equal: A modal logic for ceteris paribus preferences. Journal of philosophical logic 38(1): 83–125

    Article  Google Scholar 

  • van Benthem, J., Pacuit, E., & Roy, O. (2011). Toward a theory of play: A logical perspective on games and interaction. Games 2(1), 52–86. doi:10.3390/g2010052.

    Google Scholar 

  • van Ditmarsch, H., van de Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic. Synthese Library (Vol. 337). New York: Springer.

  • Venema, Y. (2006). Algebra and coalgebra. In Blackburn, P., van Benthem, J., & Wolter, F. (Eds.), Handbook of modal logic (pp. 331–426). Amsterdam: Elsevier

  • Zhou C. (2009) A complete deductive system for probability logic. Journal of Logic and Computation 19(6): 1427–1454

    Article  Google Scholar 

  • Zvesper J., Pacuit E. (2010) A note on assumption-completeness in modal logic. Logic and the Foundations of Game and Decision Theory–LOFT 8: 190–206

    Article  Google Scholar 

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Authors and Affiliations

  1. Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität München, Munich, Germany

    Olivier Roy

  2. TiLPS, Tilburg University, Tilburg, The Netherlands

    Eric Pacuit

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  1. Olivier Roy
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  2. Eric Pacuit
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Correspondence to Olivier Roy.

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Roy, O., Pacuit, E. Substantive assumptions in interaction: a logical perspective. Synthese 190, 891–908 (2013). https://doi.org/10.1007/s11229-012-0191-y

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  • DOI: https://doi.org/10.1007/s11229-012-0191-y

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