Abstract
This paper considers games in normal form played by Turing Machines. The machines are fed as input all the relevent information and then are required to play the game. Some ‘impossibility’ results are derived for this set-up. In particular, it is shown that no Turing Machine exists which will always play the correct strategy given its opponent's choice. Such a result also generalizes to the case in which attention is restricted to economically optimizing machines only. The paper also develops a model of knowledge. This allows the main results of the paper to be interpreted as stemming out of the impossibility of always deciding whether a player is rational or not in some appropriate sense.
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Anderlini, L. Some notes on Church's thesis and the theory of games. Theor Decis 29, 19–52 (1990). https://doi.org/10.1007/BF00134103
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DOI: https://doi.org/10.1007/BF00134103