Which one take precedence?
RHEL 7 server
For instance if i have device-mapper-libs.i686 and device-mapper-libs.x86_64 which one runs?
Do they both run?
Could this cause an performance impact?
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Those packages are just libraries, neither run by themselves. You will probably have one or more applications that are linked against those libraries; generally on RHEL7 the applications will be linked against the 64-bit version of the libraries, the 32-bit version tends to be there for backwards compatibility.
You can see if it's possible to uninstall the 32-bit version with:
rpm --test -e device-mapper-libs.i686
If it doesn't report that anything requires those libraries, you can in theory uninstall them, assuming you've installed all software through RPM. If you've compiled things from source that won't be tracked by RPM's dependencies.