Third parties in equilibrium: comment and correction

Published in a past issue of this journal, Hug (Public Choice 82:159–180, 1995) studies political competition among three vote-maximizing parties when voters cannot know exactly which policies the parties will adopt when elected. Contrary to what is claimed in Proposition 3, in the generic case the game has no Nash equilibrium in pure strategies. In this case, only a local Nash equilibrium (LNE) may exist, but due to an incorrect second order condition, the conditions in Proposition 3 do not characterize this LNE either.