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Studia Logica

, Volume 86, Issue 3, pp 353–373 | Cite as

Knowing and Supposing in Games of Perfect Information

  • Horacio Arló-Costa
  • Cristina Bicchieri
Article

Abstract

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, we do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions.

Keywords

Game Theory Hypothetical Knowledge Conditionals Common Knowledge 

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References

  1. Adams E. (1975) The logic of conditionals. Reidel, DordrechtGoogle Scholar
  2. Arló-Costa H. (1999) ‘Belief revision conditionals: basic iterated systems’. Annals of Pure and Applied Logic 96:3–28CrossRefGoogle Scholar
  3. Arló-Costa, H., and C. Bicchieri, ‘Games and Conditionals’. TARK VII, Theoretical Aspects of Rationality and Knowledge, July 22-24, 1998, Evanston, Illinois, USA, 1998.Google Scholar
  4. Arló-Costa H., Thomason R. (2001) ‘Iterative probability kinematics’. Journal of Philosophical Logic 30:479–524CrossRefGoogle Scholar
  5. Arló-Costa H. (2001) ‘Bayesian Epistemology and Epistemic Conditionals: On the Status of the Export-Import Laws’. Journal of Philosophy Vol. XCVIII 11:555–598Google Scholar
  6. Aumann R. (1995) ‘Backward induction and common knowledge of rationality’. Games and Economic Behavior 8:6–10CrossRefGoogle Scholar
  7. Battigalli P., Bonanno G. (1997) ‘The logic of belief persistence’. Economics and Philosophy 13:39–59CrossRefGoogle Scholar
  8. Bicchieri, C., and O. Schulte, ‘Common Reasoning about Admissibility,’ Erkenntnis 45 (1997).Google Scholar
  9. Bicchieri, C., and A. Antonelli, ‘Game-theoretic Axioms for Local Rationality and Bounded Knowledge,’ Journal of Logic, Language and Information 4 (1997).Google Scholar
  10. Bicchieri, C., ‘Counterfactuals, Belief Changes, and Equilibrium Refinements’, Philosophical Topics 21 (1994).Google Scholar
  11. Bicchieri C. (1989) ‘Self-Refuting Theories of Strategic Interaction: A Paradox of Common Knowledge’. Erkenntnis 30:69–85CrossRefGoogle Scholar
  12. Bicchieri C. (1988) ‘Strategic Behavior and Counterfactuals’. Synthese 76:135–169CrossRefGoogle Scholar
  13. Bicchieri C. (1988). ‘Common Knowledge and Backward Induction: A Solution to the Paradox’. In: Vardi M. (ed). Theoretical Aspects of Reasoning about Knowledge. Morgan Kaufmann Publishers, Los Altos, pp 1–5Google Scholar
  14. Bicchieri C. (1993) Rationality and Coordination. Cambridge University Press, New YorkGoogle Scholar
  15. Collins, J., ‘Newcomb’s Problem,’ 1999. http://www.columbia.edu/jdc9/download.htmlGoogle Scholar
  16. Cross, C., and D. Nute, ‘Conditional Logic,’ in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, second edition, Vol III Extensions of Classical Logic, Reidel, Dordrecht, 1998.Google Scholar
  17. Binmore K. (1996) ‘A note on Backward Induction’. Games and Economic Behavior 17: 135–37CrossRefGoogle Scholar
  18. Gärdenfors, P., ‘Conditionals and changes of belief,’ in I. Niiniluoto and R. Tuomela (eds.), The Logic and Epistemology of Scientific Change, Acta Philosophica Fennica 30 (1978), 381–404.Google Scholar
  19. Gärdenfors P. (1986) ‘Belief revisions and the Ramsey test for conditionals’. Philosphical Review 95: 81–93CrossRefGoogle Scholar
  20. Gärdenfors P. (1988) Knowledge in Flux, Bradford Book. MIT Press, Cambridge, MassGoogle Scholar
  21. Halpern, J., ‘Hypothetical knowledge and counterfactual reasoning,’ TARK VII, Theoretical Aspects of Rationality and Knowledge, July 83–97, 1998, Evanston, Illinois, USA, 1998.Google Scholar
  22. Hansson S.O.(1992) ‘In Defense of the Ramsey Test’. Journal of Philosophy 89: 522–540CrossRefGoogle Scholar
  23. Joyce J. (1999) The Foundations of Causal Decision Theory. Cambridge University Press, CambridgeGoogle Scholar
  24. Levi I. (1988) ‘Iteration of conditionals and the Ramsey test’. Synthese 76: 49–81CrossRefGoogle Scholar
  25. Lewis D. (1973) Counterfactuals. Basil Blackwell, OxfordGoogle Scholar
  26. Lewis D. (1976) ‘Probabilities of conditionals and conditional probabilities’. Philosophical Review 85: 297–315CrossRefGoogle Scholar
  27. Ramsey, F. P., Philosophical Papers, H. A. Mellor (ed.), Cambridge University Press, Cambridge, 1990.Google Scholar
  28. Samet D. (1996) ‘Hypothetical knowledge and games with perfect information’. Games and economic behavior 17 :230–251CrossRefGoogle Scholar
  29. Stalnaker R.C. (1968) ‘A theory of conditionals’, Studies in Logical Theory. American Philosophical Quarterly Monograph 2: 98–112Google Scholar
  30. Stalnaker R.C., Thomason R. (1970) ‘A semantical analysis of conditional logic’. Theoria 36: 246–281Google Scholar
  31. Rubinstein, A., Modeling Bounded Rationality, MIT Press, 1997.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of PhilosophyCarnegie-Mellon UniversityPittsburghUSA
  2. 2.University of PennsylvaniaPhiladelphiaUSA

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