For others who want to check those numbers: note that glue dominates scissors (both beat paper, lose to rock, and glue beats scissors), so scissors should never be played. With that simplification, it's an ordinary game of rock-paper-scissors, except "scissors" is now called "glue".

You mean Nash equilibrium strategy? Rock-Paper-Scissors is a zero-sum game, so Pareto optimal is a trivial notion here.

Edit (I rewrote this reply, cause it was too vague in the original :) )

Very correct in regards to every player actually having identified this (indeed, if all players are aware of the new balance, they will pick up that glue is a better type of scissors so scissors should not be picked). But imagine a player comes in and hasn't picked up this identity, while (for different reasons) they have picked up an aversion to choose rock from previous players. Then scissors still has a chance to win (against paper), and effectively rock is largely out, so the triplet scissors-paper-glue has glue as the permanent winner. This in turn (after a couple of games) is picked up and stabilizes the game as having three options for all (scissors no longer chosen), until a new player who is unaware joins.

Essentially the dynamic of the 4-choice game allows for periodic returns to a 3-choice, which is what can be used to trigger ongoing corrections to other systems.

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) ^_^