Absolute strength and stability of Elo 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 &gt;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).
No. In the general case, the ELO ratings of three people will not converge to some stable equilibrium, and here's why.
Suppose you have two players, A and B. B on average scores 66% vs A, so if they played enough games, B's ELO rating would converge to about 100 more than A's.
Now suppose we introduce player C, who scores 66% vs B on average, but never plays against player A.  If C and B play many games, their ELO difference will stabilize to about 100 as well.  If B kept playing games with A during this time, A would converge to about 100 less than B, with C about 100 more than B.
So, what happens when A finally starts playing C? For there to be stability in the ratings, we MUST have C score 76% vs A, because C is 200 ELO points higher than A.  If A scores better than that, A would gain points when playing C, causing the gap between A and B to decrease.  But then A would lose the points A gained if they started another long series with B.  In this case, the three ELO ratings are not only a function of how well they play against eachother, but also how often they play each opponent - clearly not an absolute rating in any sense.
So this begs the question, if B beats A 66% of the time, and C beats B 66% of the time, should we automatically assume that C beats A 76% of the time, as the ELO functions imply?  That doesn't sound too crazy, but for the 3 body ELO problem to be stable, this implied score would have to be accurate for ANY pair of ELO gaps between A-B and B-C.  There aren't any assumptions in the ELO model that this transitivity should work.