Is it possible to solve recursive percent equations?

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I'm working on a program that calculates the skill level of a sports teams based on how well its done against other teams. Something along the lines of, your skill is +20% of the average skill of the teams you beat.

This quickly becomes a math problem where:

x = (y+z)/2

AND

y = (x+z)/2

AND

z = (x+y)/2

Obviously, this is not good, at least in my understanding of math. Is there a way around this? Or am I trying to do something impossible and will have to figure out some way of doing this that does not result in a potential loop?

Thank you in advance.