We study a class of non-cooperative aggregative games -- denoted as \emph{social purpose games} -- in which the payoffs depend separately on a player's own strategy (individual benefits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assessment of the social benefit across players. We show that these games have a potential and we investigate its properties. We investigate the payoff structure and the uniqueness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of \emph{strict} social purpose games. Due to the nature of the partial cooperative leadership equilibrium, stable coalitions of cooperators reflect a limited form of farsightedness in their formation. As a particular application, we study the tragedy of the commons game. We show that there emerges a single stable coalition of cooperators to curb the over-exploitation of the resource.
翻译:我们研究的是一组不合作的分类游戏 -- -- 称为meph{social目的游戏} -- -- 其报酬分别取决于玩家自己的战略(个人利益)和所有玩家共同的战略概况(社会福利)的函数(社会利益),这种结构允许对各玩家之间的社会利益进行不对称评估。我们显示这些游戏具有潜力,并调查其特性。我们调查Nash equilibria 和社会opima 的报酬结构和独特性。此外,根据关于部分合作的文献,我们调查单一合作者联盟的领导作用,而其他玩家则作为不合作的追随者行事。特别是,我们表明,社会目的游戏接受一个稳定的协作者联盟的出现,用于分级的\emph{stric}社会目的游戏。由于部分合作性领导平衡的性质,稳定的协作者联盟反映了它们形成时的远见有限形式。我们特别研究共同游戏的悲剧,我们研究共同游戏的悲剧。我们显示,社会目的游戏的开发者们逐渐形成一个稳定的单一联盟。我们展示的是,在这种联盟中形成一种稳定的合作者对共同游戏的利用。