Advertisement

Synchronic Information, Knowledge and Common Knowledge in Extensive Games

  • G. Bonanno
  • P. Battigalli
Part of the Theory and Decision Library book series (TDLC, volume 20)

Abstract

The language of extensive games is complex and rich. It allows one to express such notions as the order of moves, the information a player has when it is her turn to move, etc. It is not, however, a sufficiently rich language in the sense that there are meaningful and natural statements that one can make (about a given extensive game) whose truth cannot be decided without making the language richer. We shall give two examples. Consider first the extensive form of Figure 1.

Keywords

Common Knowledge Terminal Node Extensive Form Maximum Information Strategy Profile 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann, R. (1976). Agreeing to disagree, Annals of Statistics, 4, 1236–9.CrossRefGoogle Scholar
  2. Aumann, R. and A. Brandenburger (1995). Epistemic conditions for Nash equilibrium, Econometrica, 63, 1161–1180.CrossRefGoogle Scholar
  3. Aumann, R. (1995). Backward induction and common knowledge of rationality, Games and Economic Behavior, 8, 6–19.CrossRefGoogle Scholar
  4. Bacharach, M. (1985). On a claim of Aumann in an axiomatic model of knowledge, Journal of Economic Theory, 37, 167–190.CrossRefGoogle Scholar
  5. Battigalli, P. (1987) Comportamento razionale ed equilibrio nei giochi e nelle situazioni sociali, unpublished dissertation, Università Commerciale L. Bocconi, Milan.Google Scholar
  6. Battigalli, P. and P. Guaitoli (1996). Conjectural equilibria and rationalizability in a game with incomplete information, in: P. Battigalli, A. Montesano and F. Panunzi, eds., Decisions, games and markets, Kluwer Academic Publishers, Boston.Google Scholar
  7. Benoit, J-P. and V. Krishna (1993). Renegotiation in finitely repeated games, Econometrica, 61, 303–323.CrossRefGoogle Scholar
  8. Bernheim, D., Peleg, B. and M. Whinston (1987). Coalition-proof Nash equilibria. I: Concepts, Journal of Economic Theory, 42, 1–12.CrossRefGoogle Scholar
  9. Bonanno, G. (1992a). Players’ information in extensive games, Mathematical Social Sciences, 24, 35–48.CrossRefGoogle Scholar
  10. Bonanno, G. (1992b). Rational beliefs in extensive games, Theory and Decision, 33, 153–176.CrossRefGoogle Scholar
  11. Bonanno, G. (1992c). Set-theoretic equivalence of extensive-form games, International Journal of Game Theory, 20, 429–447.CrossRefGoogle Scholar
  12. Bonanno, G. (1994). Rationally acceptable recommendations in extensive games, mimeo, University of California Davis.Google Scholar
  13. Bonanno, G. (1995). A characterization of sequential equilibrium, Economic Notes, 24, 109–128.Google Scholar
  14. Bonanno, G. (1996). On the logic of common belief, Mathematical Logic Quarterly, 42, 305–311.CrossRefGoogle Scholar
  15. Farrell, J. and E. Maskin (1989). Renegotiation in repeated games, Games and Economic Behavior, 1,327–360.CrossRefGoogle Scholar
  16. Fudenberg D. and D. Levine (1993). Self-confirming equilibrium, Econometrica, 61, 523–545.CrossRefGoogle Scholar
  17. Geanakoplos, J. (1992). Common knowledge, Journal of Economic Perspectives, 6, 53–82Google Scholar
  18. Greenberg, J. (1990). The theory of social situations, Cambridge University Press, Cambridge.Google Scholar
  19. Grossman, S. and M. Perry (1986). Perfect sequential equilibrium, Journal of Economic Theory, 39, 97–119CrossRefGoogle Scholar
  20. Halpern, J. (1986). Reasoning about knowledge: an overview, in J. Halpern Ed., Theoretical aspects of reasoning about knowledge, Morgan Kaufmann, Los Altos (California), 1–17.Google Scholar
  21. Halpern, J. and Y. Moses (1992). A guide to completeness and complexity for modal logics of knowledge and belief, Artificial intelligence, 54, 319–379.CrossRefGoogle Scholar
  22. Kalai, E. and E. Lehrer (1993a). Subjective equilibrium in repeated games, Econometrica, 61, 1231–40.CrossRefGoogle Scholar
  23. Kalai, E. and E. Lehrer (1993b). Rational learning leads to Nash equilibrium, Econometrica, 61, 1019–45.CrossRefGoogle Scholar
  24. Lismont, L. (1993). La connaissance commune en logique modale, Mathematical Logic Quarterly, 39, 115–130.CrossRefGoogle Scholar
  25. Lismont, L. and P. Mongin (1994). On the logic of common belief and common knowledge, Theory and Decision, 37 1, 75–106.CrossRefGoogle Scholar
  26. Mailath, G., L. Samuelson and J. Swinkels (1993). Extensive form reasoning in normal form games, Econometrica, 61, 273–302.CrossRefGoogle Scholar
  27. Mailath, G., L. Samuelson and J. Swinkels (1994). Normal form structures in extensive form games, Journal of Economic Theory, 64, 325–371.CrossRefGoogle Scholar
  28. Maskin, E. and J. Tirole (1994). Markov perfect equilibria, mimeo, Harvard University.Google Scholar
  29. Milgrom, P. 1981, An axiomatic characterization of common knowledge, Econometrica, 49, 219–222.CrossRefGoogle Scholar
  30. Noeldeke, G. and E. van Damme (1990). Switching away from probability one beliefs, Discussion Paper A-304, University of Bonn.Google Scholar
  31. Rubinstein, A. and A. Wolinsky (1994). Rationalizable conjectural equilibrium: between Nash and rationalizability, Games and Economic Behavior, 6, 299–311.CrossRefGoogle Scholar
  32. Selten, R. (1975). Re-examination of the perfectness concept in extensive games, International Journal of Game Theory, 4, 25–55.CrossRefGoogle Scholar
  33. Thompson, F. (1952). Equivalence of games in extensive form, Research Memorandum No. 759, The Rand Corporation.Google Scholar
  34. von Neumann, J. and O. Morgenstern (1944). Theory of games and economic behavior, Princeton University Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • G. Bonanno
  • P. Battigalli

There are no affiliations available

Personalised recommendations