In this question by "metagame" I mean a game which functions to create the rules of a sub-game.

Is there a universal metagame that would allow to create any game (including itself). Such game would be universal in a similar sense that a universal Turing machine can simulate any Turing machine (including itself).

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    Maybe something like Nomic? A game with mutable rules – Joseph Weissman Dec 30 '18 at 15:55
  • Maybe human society?! – Cyril Mikhalchenko Dec 30 '18 at 19:02
  • @Cyril What is the formal specification of this game? – Bob Dec 30 '18 at 22:10
  • The only game that makes sense in that context is Immortality. Or Perpetualis. – Bread Dec 31 '18 at 0:20
  • What is a game? Mathematical games can be pretty wild. See this for ex. en.wikipedia.org/wiki/Axiom_of_determinacy – user4894 Dec 31 '18 at 3:38

Perhaps this isn't really significantly different from a universal Turing machine. One might define a game as a Turing machine that decides who wins based on input play, and then one could create a Turing machine that takes the rules of the game (= description of the game Turing machine) as input and simulates that game. If all the input must be generated by the players, then simply add a player that chooses the rules of the game. That way we end up with a universal game Turing machine.

  • Mathematical games are way more complicated than TMs. See for ex en.wikipedia.org/wiki/Axiom_of_determinacy as I commented above. – user4894 Dec 31 '18 at 3:39
  • @user4894 Is there any proof that mathematical games cannot be modeled by Turing Machines? I didn’t see anything about that in the Wikipedia article you linked to. – Pro Q Dec 31 '18 at 9:17
  • I thought about that. But this is an encoding and I am looking for something that smells more like a game. – Bob Dec 31 '18 at 9:21
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    @ProQ I wondered the same thing even as I wrote it. I don't know and should not have made the claim. – user4894 Jan 2 '19 at 21:42

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