有限的预算连接（BBC）游戏或如何交朋友和影响的人，在预算
Bounded Budget Connection (BBC) Games or How to make friends and influence people, on a budget
摘要：
受社交网络、对等网络和覆盖网络中的应用启发，我们定义并研究了有限预算连接（BBC）博弈--我们有n个参与者或节点的集合，每个参与者或节点都有购买链接的预算，每个链接都有成本和长度，每个节点都有一组对剩余节点的偏好权重;每个节点的目标是使用其预算来购买一组输出链路，以便最小化其到剩余节点的偏好加权距离的总和。我们研究了BBC博弈中纯纳什均衡的结构和复杂性理论性质。证明了在一般的BBC博弈中确定纯纳什均衡的存在性是NP困难的。然而，在一个自然的变体，分数BBC游戏-其中允许购买链接的分数-一个纯粹的纳什均衡总是存在的。一个主要的重点是研究（n，k）-均匀BBC游戏-其中所有的链接成本，链接长度和偏好权重都相等（1），所有的预算都相等（k）。我们证明了一个纯粹的纳什均衡或稳定图存在的所有（n，k）-均匀的BBC游戏，所有的稳定图基本上是公平的（即所有节点有类似的成本）。我们提供了一个明确的建设一个家庭的稳定图，跨越频谱从最小的总社会成本最大的总社会成本。我们还研究了一个特殊的家庭，其中所有的节点模仿“相同”的购买模式，并表明，如果n是足够大的，没有这样的正则图可以是一个纯粹的纳什均衡。我们分析了最佳反应步行的配置定义的统一游戏。最后，我们扩展我们的结果的情况下，每个节点寻求最小化其最大距离到其他节点。
英文摘要：
Motivated by applications in social networks, peer-to-peer and overlay networks, we define and study the Bounded Budget Connection (BBC) game - we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set of preference weights for each of the remaining nodes; the objective of each node is to use its budget to buy a set of outgoing links so as to minimize its sum of preference-weighted distances to the remaining nodes. We study the structural and complexity-theoretic properties of pure Nash equilibria in BBC games. We show that determining the existence of a pure Nash equilibrium in general BBC games is NP-hard. However, in a natural variant, fractional BBC games - where it is permitted to buy fractions of links - a pure Nash equilibrium always exists. A major focus is the study of (n,k)-uniform BBC games - those in which all link costs, link lengths and preference weights are equal (to 1) and all budgets are equal (to k). We show that a pure Nash equilibrium or stable graph exists for all (n,k)-uniform BBC games and that all stable graphs are essentially fair (i.e. all nodes have similar costs). We provide an explicit construction of a family of stable graphs that spans the spectrum from minimum total social cost to maximum total social cost. We also study a special family of regular graphs in which all nodes imitate the "same" buying pattern, and show that if n is sufficiently large no such regular graph can be a pure Nash equilibrium. We analyze best-response walks on the configuration defined by the uniform game. Lastly, we extend our results to the case where each node seeks to minimize its maximum distance to the other nodes.
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