Not sure how to phrase this...
I am aware that Elo measures the relative strength of players.
Let's assume for this question that there is such thing as an absolute strength in chess and that players stay at their level without improving or getting worse over time.
If there are only two people in the pool playing many games against each other their Elo ratings will settle on some value and these values are a measure of their absolute strength.
Now, if there are more than two players, I was wondering, whether under the assumptions above (absolute strength exists, no change over time), the Elo ratings would also settle on constant values or would keep on changing constantly?
For the answer, I would like to exclude chess arguments like: player A cannot deal with player B's aggressive style and scores worse than against other players of the same rating (but who play more calmly).
Basically I am wondering whether there is some kind of analogue to frustration (physics term) in the Elo system, namely that, if you have >2 players in a pool they would not happily settle on a rating.
To put it concretely, I am wondering whether the system of players ends up in a steady state of constant player ratings such that if at that point in time any two players play against each other a million games, their outcome reflects exactly their rating difference.
It is assumed that players are of comparable strength so that they have a non-zero probability to draw (or win).