论文标题
彭尼游戏中的不同意和在戒指，网络，社区和城市中随机散步
Intransitiveness in the Penney Game and in Random Walks on rings, networks, communities and cities
论文作者
论文摘要
游戏的不同意性概念，这是没有第一手赢得策略的条件，就像彭尼（Penney）游戏一样，头部或尾巴的延伸。由于可以将游戏转换为图表上的随机步行，即马尔可夫过程，因此我们将不及力的概念扩展到了此类系统。游戏的结尾通常包括出现预定义的模式。在随机步行的语言中，这对应于一个吸收陷阱，因为一旦游戏达到了这种情况，游戏就结束了。因此，可以将游戏的不同意映射到陷阱之间的竞争问题中。我们详细介绍了几种网络（环，无尺度，等级和城市风格的环）的随机步行者，并具有多种变化：陷阱可能会被部分吸收，步行者可能会偏置，并且初始分布可以任意。我们发现，传递性概念对于表征图和步行者的组合特性非常有用。
The concept of intransitiveness for games, which is the condition for which there is no first-player winning strategy can arise surprisingly, as happens in the Penney game, an extension of the heads or tails. Since a game can be converted into a random walk on a graph, i.e., a Markov process, we extend the intransitiveness concept to such systems. The end of the game generally consists in the appearance of a pre-defined pattern. In the language of random walk this corresponds to an absorbing trap, since once that the game has reached this condition the game comes to an end. Therefore, the intransitiveness of the game can be mapped into a problem of competition among traps. We analyse in details random walkers on several kind of networks (rings, scale-free, hierarchical and city-inspired) with several variations: traps can be partially absorbing, the walker can be biased and the initial distribution can be arbitrary. We found that the transitivity concept can be quite useful for characterizing the combined properties of a graph and that of the walkers.
