This paper studies the computation of pure Nash equilibrium (PNE) in network utility-sharing and discretized Hotelling–Downs games, and the interplay between these classes of games. First, we introduce and study a variant of network utility-sharing games with additional player-specific non-shareable costs (NUSG+), which is shown to possess a PNE. We extend polynomial-time PNE computation results to a class of graphs that generalizes series-parallel graphs when the non-shareable costs are player-independent. Second, a spatial election game is introduced with a discretized utility function. The complexity of this game is shown to be in Polynomial Local Search, and a polynomial-time PNE computation is derived for certain settings. Third, a spatio-temporal election game model is presented based on an NUSG+ when voter opinions form natural discrete clusters. This model captures several variants of the classic Hotelling–Downs election model, including ones with limited attraction, ability of candidates to enter, change stance positions and exit any time during the campaign or abstain from the race, the restriction on candidates to access certain stance positions, and the operational costs of running a campaign. Finally, we provide a polynomial-time PNE computation for an election game when stance changes are restricted.

本文研究了网络效用共享和离散的Hotelling-Downs游戏中纯Nash平衡（PNE）的计算，以及这些类游戏之间的相互作用。首先，我们介绍并研究一种网络实用程序共享游戏的变体，其中包含特定于玩家的不可分摊的额外费用（NUSG +），这表明它具有PNE。我们将多项式时间PNE计算结果扩展到一类图，当不可分摊的成本与玩家无关时，该图可以概括一系列平行图。其次，引入具有离散效用函数的空间选举游戏。该游戏的复杂性显示在多项式局部搜索中，并且针对某些设置推导了多项式时间PNE计算。第三，基于一个NUSG +呈现时空选游戏模型时选举人意见形成自然离散簇。该模型捕获了经典的Hotelling–Downs选举模型的多种变体，包括吸引力有限，候选人在竞选期间任何时候可以进入，更改立场立场和退出或在比赛中弃权的能力，候选人对某些立场的限制等。位置以及开展广告系列的运营成本。最后，当姿态改变受到限制时，我们为选举游戏提供多项式时间PNE计算。对候选人进入某些立场职位的限制，以及竞选活动的运营成本。最后，当姿态改变受到限制时，我们为选举游戏提供多项式时间PNE计算。对候选人进入某些立场职位的限制，以及竞选活动的运营成本。最后，当姿态改变受到限制时，我们为选举游戏提供多项式时间PNE计算。