Caching networks can reduce the routing costs of accessing contents by caching contents closer to users. However, cache nodes may belong to different entities and behave selfishly to maximize their own benefits, which often lead to performance degradation for the overall network. While there has been extensive literature on allocating contents to caches to maximize the social welfare, the analysis of selfish caching behaviors remains largely unexplored. In this paper, we model the selfish behaviors of cache nodes as selfish caching games on arbitrary directed graphs with heterogeneous content popularity. We study the existence of a pure strategy Nash equilibrium (PSNE) in selfish caching games, and analyze its efficiency in terms of social welfare. We show that a PSNE does not always exist in arbitrary-topology caching networks. However, if the network does not have a mixed request loop, i.e., a directed loop in which each edge is traversed by at least one content request, we show that a PSNE always exists and can be found in polynomial time. Furthermore, we can avoid mixed request loops by properly choosing request forwarding paths. We then show that the efficiency of Nash equilibria, captured by the price of anarchy (PoA), can be arbitrarily poor if we allow arbitrary content request patterns, and adding extra cache nodes can make the PoA worse, i.e., cache paradox happens. However, when cache nodes have homogeneous request patterns, we show that the PoA is bounded even allowing arbitrary topologies. We further analyze the selfish caching games for cache nodes with limited computational capabilities, and show that an approximate PSNE exists with bounded PoA in certain cases of interest. Simulation results show that increasing the cache capacity in the network improves the efficiency of Nash equilibria, while adding extra cache nodes can degrade the efficiency of Nash equilibria.

中文翻译：

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有向图上的自私缓存游戏

缓存网络可以通过将内容缓存到更接近用户的位置来降低访问内容的路由成本。但是，缓存节点可能属于不同的实体，并且会自私地发挥作用以最大化其自身的利益，这通常会导致整个网络的性能下降。尽管已有大量文献将内容分配给缓存以最大程度地提高社会福利，但对自私缓存行为的分析仍未得到充分探索。在本文中，我们将缓存节点的自私行为建模为具有异构内容流行度的任意有向图上的自私缓存游戏。我们研究了自私缓存游戏中纯策略纳什均衡（PSNE）的存在，并从社会福利角度分析了其效率。我们显示PSNE并不总是存在于任意拓扑缓存网络中。然而，如果网络没有混合请求循环，即每个边缘至少被一个内容请求遍历的有向循环，则表明PSNE始终存在并且可以在多项式时间内找到。此外，我们可以通过适当选择请求转发路径，避免混杂的请求循环。然后，我们表明，如果允许任意内容请求模式，则无政府状态（PoA）的价格所捕获的Nash均衡的效率可能会很差，并且添加额外的缓存节点会使PoA恶化，即发生缓存悖论。但是，当高速缓存节点具有同类请求模式时，我们表明PoA甚至可以允许任意拓扑，因此是有界的。我们进一步分析了计算能力有限的缓存节点的自私缓存游戏，并表明在某些感兴趣的情况下，存在带有受限PoA的近似PSNE。仿真结果表明，增加网络中的缓存容量可以提高Nash均衡的效率，而增加额外的缓存节点则可以降低Nash均衡的效率。