Penney博弈与环、网络、社区及城市上随机游走中的非传递性
Intransitiveness in the Penney Game and in Random Walks on rings, networks, communities and cities
AI总结：
本研究将Penney博弈中的非传递性概念拓展至图上随机游走系统，将其映射为陷阱竞争问题，分析了多种网络与不同游走条件下的情况，发现传递性可有效刻画图与游走者的组合性质。
摘要：
博弈中的非传递性概念（即不存在先手必胜策略的情形）会以出人意料的方式出现，正如Penney博弈（抛硬币游戏的一种拓展）中所呈现的那样。由于博弈可被转化为图上的随机游走（即一种马尔可夫过程），我们将非传递性概念拓展至这类系统中。博弈的结束通常以某一预设模式的出现为标志，在随机游走的语境下，这对应一个吸收陷阱——因为一旦博弈达到该条件，就会立即终止。因此，博弈的非传递性可被映射为陷阱间的竞争问题。我们详细分析了多种网络（环、无标度网络、层级网络和城市启发型网络）上的随机游走者，并设置了多种变量条件：陷阱可为部分吸收型、游走者可存在偏置、初始分布可为任意形式。我们发现，传递性概念对于刻画图与游走者的组合性质颇具实用价值。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
