论文标题
定期合作
Cooperation in regular lattices
论文作者
论文摘要
在进化游戏理论的背景下，支持合作的最值得注意的机制之一是空间互惠，通常是通过在空间结构中分配玩家，使合作者可以将合作者聚集在一起并避免剥削。这就提出了一个重要的问题：合作的生存如何受到不同拓扑影响？在这里，为了解决这个问题，我们在几个常规格子上探索了焦点公共物品（FPGG）和经典公共物品游戏（PGG）以及囚犯的困境（PD）：蜂窝，广场（与von Neumann和Moore社区），Kagome，Kagome，Kagome，Triangular，Cubic，Cubic，Cubic，以及4D超纤维lattices使用分析型和代理基准MONEDERED CARTECENTINCE CARTECTIONS CARTECTIONS。我们发现，对于这两种公共产品游戏，在所有二维晶格上都出现了一致的趋势：随着第一邻居的数量增加，合作得到了增强。但是，仅通过根据收益的协同因素按连接数量归一化的协同因素来分析结果。除此之外，聚集的拓扑，即允许两个连接球员共享邻居的拓扑，这是FPGG合作最有益的。对于经典的PGG而言，并非总是如此，在这些PGG之间共享互联玩家之间的邻居可能会或可能不会使合作受益。我们还通过将这种类别游戏的晶格结构表示为单个互动游戏，将经典PGG重新解释为焦点游戏，具有更长的加权社区，这是对任何常规晶格拓扑的有效方法。最后，我们表明，根据PD的回报参数化，PD和FPGG之间可能存在等效。当两款游戏之间的映射不完善时，有效协同参数的定义仍然可以显示出它们的相似性。
In the context of Evolutionary Game Theory, one of the most noteworthy mechanisms to support cooperation is spatial reciprocity, usually accomplished by distributing players in a spatial structure allowing cooperators to cluster together and avoid exploitation. This raises an important question: how is the survival of cooperation affected by different topologies? Here, to address this question, we explore the Focal Public Goods (FPGG) and classic Public Goods Games (PGG), and the Prisoner's Dilemma (PD) on several regular lattices: honeycomb, square (with von Neumann and Moore neighborhoods), kagome, triangular, cubic, and 4D hypercubic lattices using both analytical methods and agent-based Monte Carlo simulations. We found that for both Public Goods Games, a consistent trend appears on all two-dimensional lattices: as the number of first neighbors increases, cooperation is enhanced. However, this is only visible by analysing the results in terms of the payoff's synergistic factor normalized by the number of connections. Besides this, clustered topologies, i.e., those that allow two connected players to share neighbors, are the most beneficial to cooperation for the FPGG. The same is not always true for the classic PGG, where having shared neighbors between connected players may or may not benefit cooperation. We also provide a reinterpretation of the classic PGG as a focal game by representing the lattice structure of this category of games as a single interaction game with longer-ranged, weighted neighborhoods, an approach valid for any regular lattice topology. Finally, we show that depending on the payoff parametrization of the PD, there can be an equivalency between the PD and the FPGG; when the mapping between the two games is imperfect, the definition of an effective synergy parameter can still be useful to show their similarities.
