You may be interested in alpha-rank. It’s an Elo-esque system for highly ‘nontransitive’ games—ie, games where there’re lots of rock-paper-scissors-esque cycles.
At a high level, what it does is set up a graph like the one you’ve drawn, then places a token on a random node and repeatedly follows the ‘defeated-by’ edges. The amount of time spent on a node gives the strength of the strategy.
My own interest in recollecting this variation (an actual thing, from my childhood years) is that intuitively it seems to me that this type of limited setting may be enough so that the inherent dynamic of ‘new player will go for the less than optimal strategy’, and the periodic ripple effect it creates, can (be made to) mimic some elements of a formal logic system, namely the interactions of non-sentences with sentences.
So I posted this as a possible trigger for more reflection, not for establishing the trivial (optimal strategy in this corrupted variation of the game) ^_^
You may be interested in alpha-rank. It’s an Elo-esque system for highly ‘nontransitive’ games—ie, games where there’re lots of rock-paper-scissors-esque cycles.
At a high level, what it does is set up a graph like the one you’ve drawn, then places a token on a random node and repeatedly follows the ‘defeated-by’ edges. The amount of time spent on a node gives the strength of the strategy.
You might also be interested in rectified policy space response oracles, which is one approach to finding new, better strategies in nontransitive games.
Thank you, I will have a look!
My own interest in recollecting this variation (an actual thing, from my childhood years) is that intuitively it seems to me that this type of limited setting may be enough so that the inherent dynamic of ‘new player will go for the less than optimal strategy’, and the periodic ripple effect it creates, can (be made to) mimic some elements of a formal logic system, namely the interactions of non-sentences with sentences.
So I posted this as a possible trigger for more reflection, not for establishing the trivial (optimal strategy in this corrupted variation of the game) ^_^