Advertisement

International Journal of Game Theory

, Volume 9, Issue 3, pp 157–167 | Cite as

On repeated games with incomplete information played by non-Bayesian players

  • N. Megiddo
Papers

Abstract

Unlike in the traditional theory of games of incomplete information, the players here arenot Bayesian, i.e. a player does not necessarily have any prior probability distribution as to what game is being played. The game is infinitely repeated. A player may be absolutely uninformed, i.e. he may know only how many strategies he has. However, after each play the player is informed about his payoff and, moreover, he has perfect recall. A strategy is described, that with probability unity guarantees (in the sense of the liminf of the average payoff) in any game, whatever the player could guarantee if he had complete knowledge of the game.

Keywords

Probability Distribution Economic Theory Game Theory Prior Probability Incomplete Information 
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.J., andM. Maschler: Repeated Games with Incomplete Information: The Zero-Sum Extensive Case. Report to the U.S. Arms Control and Disarmament Agency, Washington, D.C. Final report on Contract ACDA/ST-143, prepared by Mathematica, Chapter III, Princeton 1968, 25–108.Google Scholar
  2. Baños, A.: On Pseudo-Games. The Annals of Mathematical Statistics39, 1968, 1932–1945.Google Scholar
  3. Feller, W.: An Introduction to Probability Theory and its Applications. Vol. 1, New York 1957.Google Scholar
  4. Harsanyi, J.C.: Games with Incomplete Information Played by ‘Bayesian’ Players. Management Science14, 1967–68, 159–182, 320–334, 486–502.Google Scholar
  5. Kohlberg, E.: Optimal Strategies in Repeated Games with Incomplete Information. International J. Game Theory4, 1975a, 7–24.Google Scholar
  6. —: The Information Revealed in Infinitely Repeated Games of Incomplete Information. International J. Game Theory4, 1975b, 57–59.Google Scholar
  7. Megiddo, N.: On Repeated Games with Incomplete Information Played by Non-Bayesian Players. Discussion Paper No. 373, The Center for Mathematical Studies in Economics and Management Sciences, Northwestern University, March 1979.Google Scholar
  8. Mertens, J.F.: The Value of Two-Person Zero-Sum Repeated Games: The Extensive Case. International J. Game Theory1, 1971–72, 217–227 continued in2, 1973, 231–234.Google Scholar
  9. Mertens, J.F., andS. Zamir: The Value of Two-Person Repeated Games with Lack of Information on Both Sides. International J. Game Theory1, 1971–72, 39–64.Google Scholar
  10. Ponssard, J.P., andS. Zamir: Zero-Sum Sequential Games with Incomplete Information. International J. Game Theory2, 1973, 99–107.Google Scholar
  11. Stearns, R.E.: A Formal Concept of Games of Incomplete Information. Report to the U.S. Arms Control and Disarmament Agency, Washington, D.C. Final report on Contract ACDA/ST-116 prepared by Mathematica, Chapter IV, Princeton 1967, 405–433.Google Scholar
  12. Titchmarsh, E.G.: The Theory of Functions. 2nd Edition. Oxford 1939, 226–229.Google Scholar
  13. Widder, D.V.: The Laplace Transform. Princeton 1941.Google Scholar
  14. Zamir, S.: On the Relation Between Finitely and Infinitely Repeated Games with Incomplete Information. International J. Game Theory1, 1971–72, 179–198.Google Scholar
  15. —: On Repeated Games with General Information Function. International J. Game Theory2, 1973, 215–229.Google Scholar

Copyright information

© Physica-Verlag 1980

Authors and Affiliations

  • N. Megiddo
    • 1
  1. 1.Statistics DepartmentTel Aviv UniversityTel AvivIsrael

Personalised recommendations