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If you play only against each other, and split every other game, your ratings will oscillate then eventually become equal.
But along the way, the ratings functions will look like a carrier wave enveloping another signal.
You might be -17, +19, -15, +17, -13, +15 ... with an odd-even cancelation kicking in at some point too.
There are 2 numbers per opponent: rating, and rating deviation (rd). The rating number is published, the rd is part of a hidden calculation.
Your rd governs the rate of change of your rating more than the individual combat against another player.
If you lose your first 30 games against the lowest rated people on here, then win 30 games in a row against the highest rated people on here, your rating would still be near the middle of the pack.
If you won your first 30 games against the top players on here, then lost your next 30 games against the lowest rated players on here, your rating would be much higher.