I think that the phrase
your and your competitors’ relative market performance
is a pretty odd fish in the first place—because performance comes out singular here even though the actual subject being discussed is at least two instances of performance (yours and your competitors', the latter of which may be tracked as a set of grouped and averaged numbers or as multiple sets of individual numbers, one for each competitor) considered relative to each other.
In the more normal case, the noun at the end of the phrase would be plural, as in
your and your girlfriend's fathers
and most people (I suspect) would feel absolutely no temptation to express that relationship as
you and your girlfriend's fathers
your and your girlfriend's father
you and your girlfriend's father
So the real culprit here is "relative performance," which invites us to understand it as referring to one performance that both you and your competitors share, rather than as referring to two (or more) sets of performance data matched against one another. The expression is idiomatically legitimate—indeed, completely normal—but that doesn't make it any less of an impediment to recognizing the real-world comparison that underlies the expression in this instance.
Even in that case, however, any inclination to choose against the replicated possessive in "your and your competitors'" recedes if we recast the conversation as being about matching our performance and our competitors' performance. Would anyone argue in favor of
identifying us and our competitors’ relative market performance
identifying our and our competitors’ relative market performance
? I wouldn't. That the wording is "your and your competitors'" instead of "our and our competitors'" is of no syntactical importance to whether the first word should take the form of a possessive.
I can't think of any plausible argument for adopting the wording "you and your competitor's market performance" or "us and our competitor's market performance" in preference to "your and your competitor's market performance" or "our and our competitor's market performance."