Economic Theory

, Volume 6, Issue 3, pp 453–467 | Cite as

Depth of knowledge and the effect of higher order uncertainty

  • Stephen Morris
  • Andrew Postlewaite
  • Hyun Song Shin
Research Articles

Summary

A number of recent papers have highlighted the importance of uncertainty about others' information in models of asymmetric information. We introduce a notion that reflects the depth of knowledge in an information system. We show how the depth of knowledge can be used to bound the effect of higher order uncertainty in certain problems. We further provide bounds on the size of bubbles in finite horizon rational expectations models where the bounds depend on the depth of knowledge.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abel, A., Mailath, G.: Financing losers in competitive markets. J. Financ. Intermed.3, 139–165 (1994)Google Scholar
  2. Allen, F., Morris, S., Postlewaite, A.: Finite bubbles with short sales constraints and asymmetric information. J. Econ. Theory61, 206–230 (1993)Google Scholar
  3. Aumann, R.: Agreeing to disagree. Ann. Stat.4, 1236–1239 (1976)Google Scholar
  4. Aumann, R.: Irrationality in game theory. In: Dasgupta, P., Gale, D., Hart, O., Maskin, E. (eds.) Economic analysis of markets and games: Essays in honor of Frank Hahn. Cambridge: MIT Press 1992Google Scholar
  5. Aumann, R., Brandeburger, A.: Epistemic conditions for Nash equilibrium. Harvard Business School working paper 91–042, 1991Google Scholar
  6. Bacharach, M.: Some extensions of a claim of Aumann in an axiomatic model of knowledge. J. Econ. Theory37, 167–190 (1985)Google Scholar
  7. Brandenburger, A., Dekel, E.: Hierarchies of beliefs and common knowledge. J. Econ. Theory59, 189–198 (1993)Google Scholar
  8. Geanakoplos, J.: Common knowledge. J. Econ. Perspect.6, 53–82 (1992)Google Scholar
  9. Haifetz, A., Samet, D.: Universal partition structures. Mimeo, Tel Aviv Business School, 1993Google Scholar
  10. Halpern, J.: Reasoning about knowledge: An overview. In: Theoretical aspects of reasoning about knowledge: proceedings of the 1986 conference. Los Altos: Morgan Kaufman 1986Google Scholar
  11. Harsanyi, J.: Games with incomplete information played by “Bayesian” players I-III. Manage. Sci.14, 159–182;14, 320–334;14, 486–502 (1967/1968)Google Scholar
  12. Kraus, A., Smith, M.: Market created risk. J. Finance44, 557–569 (1990)Google Scholar
  13. Kreps, D., Milgrom, P., Roberts, J., Wilson, R.: Rational cooperation in the finitely repeated prisoners' dilemma. J. Econ. Theory27, 245–252 (1982)Google Scholar
  14. Mertens, J.-F., Zamir, S.: Formulation of Bayesian analysis for games with incomplete information. Int. J. Game Theory14, 1–29 (1985)Google Scholar
  15. Milgrom, P.: An axiomatic characterization of common knowledge.Econometica 49, 219–222 (1981)Google Scholar
  16. Milgrom, P., Stokey, N.: Information, trade and common knowledge. J. Econ. Theory26, 17–27 (1982)Google Scholar
  17. Milgrom, P., Roberts, J.: Predation, reputation and entry deterrence. J. Econ. Theory27, 280–312 (1982)Google Scholar
  18. Monderer, D., Samet, D.: Approximating common knowledge with common beliefs. Games Econ. Behav.1, 170–190 (1989)Google Scholar
  19. Morris, S.: Trade with heterogeneous prior beliefs and asymmetric information. Econometrica62, 1327–1347 (1994)Google Scholar
  20. Morris, S., Rob, R., Shin, H.: p-Dominance and belief potential. Econometrica63, 145–157 (1995)Google Scholar
  21. Rubinstein, A.: The electronic mail game: Strategic behavior under ‘almost common knowledge’. Am. Econ. Rev.79, 385–391 (1989)Google Scholar
  22. Sebenius, J., Geanakoplos, J.: Don't bet on it: Contingent agreements with asymmetric information. J. Am. Stat. Assoc.78, 424–426 (1983)Google Scholar
  23. Shin, H.: Logical structure of common knowledge. J. Econ. Theory60, 1–13 (1993)Google Scholar
  24. Shin, H., Williamson, T.: How much common belief is necessary for a convention? CARESS Working Paper #92-32, University of Pennsylvania, 1992. Forthcoming in Games and Econ. Behav. (1995)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Stephen Morris
    • 1
  • Andrew Postlewaite
    • 1
  • Hyun Song Shin
    • 2
  1. 1.Department of EconomicsUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Department of EconomicsUniversity of SouthamptonSouthamptonEngland

Personalised recommendations