Incomplete Information Games with Transcendental Values
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.
Volume (Year): 6 (1981)
Issue (Month): 2 (May)
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