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.

翻译：我们研究Boehmer等人（IJCAI 2021）提出的时序图上的Voronoi博弈，其中两个玩家各自选择时序图中的一个顶点，目标是比对手更早到达其他顶点。本文考虑时间逆序Voronoi博弈，即玩家希望最大化能在她之前到达她的顶点数量。由于时序图中的时间距离一般不具有对称性，这构成了一个不同的博弈。我们针对各类时序图（包括时序树、环、网格、团和分裂图）中纳什均衡的存在性，研究这两类博弈的差异。广泛结果表明，这两类博弈的行为确实因所考虑的时序图类别不同而呈现显著差异。