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Incomplete information games with transcendental values

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  • MERTENS, Jean-François
  • ZAMIR, Shmuel

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.
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Suggested Citation

  • MERTENS, Jean-François & ZAMIR, Shmuel, 1981. "Incomplete information games with transcendental values," CORE Discussion Papers RP 445, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:445
    Note: In : Mathematics of Operations Research, 6(2), 313-318, 1981
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    File URL: http://dx.doi.org/10.1007/BF01753433
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