What is the overlap between the Gaia and the Hipparcos catalog? Is there any kind of concordance available between the sources in the Hipparcos catalog and the Gaia DR2 catalog? I.e., mapping the Gaia DR2 source_id to the Hipparcos HIP number?
As part of the Gaia DR2, cross-matches to several catalogues including HIP2 were included. The main reference for this is Marrese et al. (2018) "Gaia Data Release 2. Cross-match with external catalogues: algorithms and results". The resultant matches are included in the tables gaiadr2.hipparcos2_best_neighbour and gaiadr2.hipparcos2_neighbourhood available via the query facilities in the Gaia Archive.

Unfortunately the match is not particularly complete and it is not entirely clear why. From the paper:


  While we expect to find Gaia counterparts for most of the Hipparcos2 sources, with the exception of the brightest ones, the
  cross-match results include only about two-thirds of them. This
  means that according to the adopted cross-match algorithm, only
  about two-thirds of the Hipparcos2 objects have a Gaia counterpart that is compatible within the position errors (i.e. have at least
  one good neighbour). Hence the Hipparcos2 cross-match results
  clearly show an issue that needs to be investigated.


As a result, they also provide a table of cross-matches based on a 1-arcsecond cone search, available on the Gaia DR2 known issues page. This cross-match is a lot more complete, but there are still a few objects that are present in both catalogues that are missing. Several of these are nevertheless present in SIMBAD, e.g. 85&nbsp;Pegasi = HIP&nbsp;171 = Gaia&nbsp;DR2&nbsp;2853900872207150720.