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Incomplete Information Games with Transcendental Values

Author

Listed:
  • Jean-François Mertens

    (Center for Operations Research and Econometrics, Catholic University of Louvain, Louvain-La-Neuve, Belgium)

  • Shmuel Zamir

    (Center for Operations Research and Econometrics, Catholic University of Louvain, Louvain-La-Neuve, Belgium)

Abstract

In a repeated zero-sum two-person game with incomplete information on both sides, the asymptotic value is defined as v = lim n (rightarrow)(infinity) v n , where v n is the value of the game with n repetitions. It is shown here that v may be a transcendental number even for games in which all parameters defining the game are rational. This is in contrast to the situation in stochastic games where by the result of Bewley-Kohlberg (Bewley, T., E. Kohlberg. 1976. The asymptotic theory of stochastic games. Math. Oper. Res. 1 197--208.) v is algebraic. This indicates a fundamental difference between stochastic games and repeated games with incomplete information.

Suggested Citation

  • Jean-François Mertens & Shmuel Zamir, 1981. "Incomplete Information Games with Transcendental Values," Mathematics of Operations Research, INFORMS, vol. 6(2), pages 313-318, May.
  • Handle: RePEc:inm:ormoor:v:6:y:1981:i:2:p:313-318
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    File URL: http://dx.doi.org/10.1287/moor.6.2.313
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    References listed on IDEAS

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    1. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
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