  A measurement of the top quark-antiquark pair production cross section
$\sigma_{\mathrm{t\overline{t}}}$ in proton-proton collisions at a
centre-of-mass energy of 13 TeV is presented. The data correspond to an
integrated luminosity of 35.9 fb$^{-1}$, recorded by the CMS experiment at the
CERN LHC in 2016. Dilepton events (e$^\pm\mu^\mp$, $\mu^+\mu^-$, e$^+$e$^-$)
are selected and the cross section is measured from a likelihood fit. For a top
quark mass parameter in the simulation of $m^{\mathrm{MC}}_{\mathrm{t}} =$
172.5 GeV the fit yields a measured cross section
$\sigma_{\mathrm{t\overline{t}}} =$ 803 $\pm$ 2 (stat) $\pm$ 25 (syst) $\pm$ 20
(lumi) pb, in agreement with the expectation from the standard model
calculation at next-to-next-to-leading order. A simultaneous fit of the cross
section and the top quark mass parameter in the POWHEG simulation is performed.
The measured value of $m^{\mathrm{MC}}_{\mathrm{t}} =$ 172.33 $\pm$ 0.14 (stat)
$^{+0.66}_{-0.72}$ (syst) GeV is in good agreement with previous measurements.
The resulting cross section is used, together with the theoretical prediction,
to determine the top quark mass and to extract a value of the strong coupling
constant with different sets of parton distribution functions.
