偏好博弈与个性化均衡及其在分数BGP中的应用
Preference Games and Personalized Equilibria, with Applications to Fractional BGP
摘要：
本文研究了两类基于流的网络博弈-分数BGP（边界网关协议）博弈和分数BBC（有界预算连接）博弈的均衡计算复杂性。BGP是将互联网保持在一起的粘合剂，因此其稳定性，即分数BGP游戏（Haxell，Wilfong）的均衡，是具有实际重要性的问题。BBC游戏（Laoutaris等人）遵循了网络形成游戏的大量工作的传统，并捕获了从社交网络和覆盖网络到对等网络的各种应用。本文的中心结果是，有没有完全多项式时间近似计划（除非PPAD是在FP）计算分数BGP游戏和分数BBC游戏的平衡。我们通过证明一个新的和令人惊讶的简单的游戏，分数偏好游戏，这是可还原的分数BGP和BBC游戏的硬度。我们定义了一个新的流动为基础的矩阵游戏的平衡概念-个性化的平衡-推广分数BBC和分数BGP游戏。我们不仅证明了存在性，而且证明了所有矩阵博弈都存在理性的个性化均衡，这意味着分数BGP和BBC博弈也存在理性均衡。特别是，这提供了一个替代的证明和加强的主要结果[Haxell，Wilfong]。对于k-玩家矩阵游戏，其中k = 2，我们提供了一个组合特征，导致一个多项式时间算法计算所有个性化的均衡。当k >= 5时，我们证明了个性化均衡是PPAD-难以在完全多项式时间内近似的.我们相信个性化均衡的概念具有现实意义。
英文摘要：
We study the complexity of computing equilibria in two classes of network games based on flows - fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet together and hence its stability, i.e. the equilibria of fractional BGP games (Haxell, Wilfong), is a matter of practical importance. BBC games (Laoutaris et al) follow in the tradition of the large body of work on network formation games and capture a variety of applications ranging from social networks and overlay networks to peer-to-peer networks. The central result of this paper is that there are no fully polynomial-time approximation schemes (unless PPAD is in FP) for computing equilibria in both fractional BGP games and fractional BBC games. We obtain this result by proving the hardness for a new and surprisingly simple game, the fractional preference game, which is reducible to both fractional BGP and BBC games. We define a new flow-based notion of equilibrium for matrix games -- personalized equilibria -- generalizing both fractional BBC and fractional BGP games. We prove not just the existence, but the existence of rational personalized equilibria for all matrix games, which implies the existence of rational equilibria for fractional BGP and BBC games. In particular, this provides an alternative proof and strengthening of the main result in [Haxell, Wilfong]. For k-player matrix games, where k = 2, we provide a combinatorial characterization leading to a polynomial-time algorithm for computing all personalized equilibria. For k >= 5, we prove that personalized equilibria are PPAD-hard to approximate in fully polynomial time. We believe that the concept of personalized equilibria has potential for real-world significance.
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