  We study Voronoi games on temporal graphs as introduced by Boehmer et al.
(IJCAI 2021) where two players each select a vertex in a temporal graph with
the goal of reaching the other vertices earlier than the other player. In this
work, we consider the reverse temporal Voronoi game, that is, a player wants to
maximize the number of vertices reaching her earlier than the other player.
Since temporal distances in temporal graphs are not symmetric in general, this
yields a different game. We investigate the difference between the two games
with respect to the existence of Nash equilibria in various temporal graph
classes including temporal trees, cycles, grids, cliques and split graphs. Our
extensive results show that the two games indeed behave quite differently
depending on the considered temporal graph class.
