So by the end Glue is almost never chosen, while Rock reverts to being a regular option which risks defeat by paper, that in time becomes more popular.
This sentence confuses me. It seems to me like you’re implying that there is a time when the probability of choosing rock exceeds the probability of choosing glue when in fact the Nash equilibrium strategy is 13 rock, 13 paper, 13 glue and 03 scissors.
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”.
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.
Regardless of what the new player does, there is no reason to ever play scissors. I don’t see any interesting “4-choice dynamic” here. Perhaps you should pick a different example with multiple Nash equilibria.
You are confusing “reason to choose” (which is obviously not there; optimal strategy is trivial to find) with “happens to be chosen”. Ie you are looking at what is said from an angle which isn’t crucial to the point.
Everyone is aware that scissors is not be chosen at any time if the player has correctly evaluated the dynamic. Try asking a non-sentence in a formal logic system to stop existing cause it evaluated the dynamic, and you’ll get why your point is not sensible.
This sentence confuses me. It seems to me like you’re implying that there is a time when the probability of choosing rock exceeds the probability of choosing glue when in fact the Nash equilibrium strategy is 13 rock, 13 paper, 13 glue and 03 scissors.
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”.
Please read my edited reply to lsusr.
You mean Nash equilibrium strategy? Rock-Paper-Scissors is a zero-sum game, so Pareto optimal is a trivial notion here.
Fixed.
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.
Regardless of what the new player does, there is no reason to ever play scissors. I don’t see any interesting “4-choice dynamic” here. Perhaps you should pick a different example with multiple Nash equilibria.
You are confusing “reason to choose” (which is obviously not there; optimal strategy is trivial to find) with “happens to be chosen”. Ie you are looking at what is said from an angle which isn’t crucial to the point.
Everyone is aware that scissors is not be chosen at any time if the player has correctly evaluated the dynamic. Try asking a non-sentence in a formal logic system to stop existing cause it evaluated the dynamic, and you’ll get why your point is not sensible.