Woods and other incumbent directors phoned big institutional shareholders such as BlackRock, State Street and the Vanguard Group, trying to persuade them to vote against the Engine No. 1 slate, the hedge fund alleged. Engine No. 1, founded by Silicon Valley veteran Chris James, had spent “tens of millions” of dollars on its proxy fight, and James believed ExxonMobil had done the same. ExxonMobil told the big shareholders to divide their votes so that the Engine No. 1 candidates, in particular Karsner and Anders Runevad, former chief executive of Vestas Wind Systems, would fall short. Vanguard voted for two of the nominees with oil refining experience, Gregory Goff and Kaisa Hietala, but not Karsner or Runevad. BlackRock voted for all but Runevad.