Handbook of Liturgical Practice of the Russian Church Abroad
While technically the presiding Priest (whoever is standing at the front of the Holy Table) would always bestow the peace throughout the whole of the Liturgy, it has long been the normal practice within the Church Abroad that when Priests concelebrate, the peace is bestowed upon the people by whichever Priest has pronounced the exclamation just before it — thus ‘sharing’ this act between the various Priests across the service. This is blessed as the normal practice for our Diocese.
This is not to be done, however, when an Abbot or Archimandrite serves within his own monastery. In this case the Abbot always bestows the peace.
(For more information on why certain elements of the Divine Liturgy are reserved to the chief celebrant Priest alone, see additional notes in the Handbook entry on the Prayer of the Cherubic Hymn during concelebrations.)