Multilevel Network Games
WEB AND INTERNET ECONOMICS(2014)
摘要
We consider a multilevel network game, where nodes can improve their communication costs by connecting to a high-speed network. The n nodes are connected by a static network and each node can decide individually to become a gateway to the high-speed network. The goal of a node v is to minimize its private costs, i.e., the sum (SUM-game) or maximum (MAX-game) of communication distances from v to all other nodes plus a fixed price alpha > 0 if it decides to be a gateway. Between gateways the communication distance is 0, and gateways also improve other nodes' distances by behaving as shortcuts. For the SUM-game, we show that for alpha <= n - 1, the price of anarchy is Theta (n/root alpha) and in this range equilibria always exist. In range alpha is an element of (n-1, n(n-1)) the price of anarchy is Theta(root alpha), and for alpha >= n(n - 1) it is constant. For the MAX-game, we show that the price of anarchy is either Theta(1 + n/root alpha), for alpha >= 1, or else 1. Given a graph with girth of at least 4 alpha, equilibria always exist. Concerning the dynamics, both games are not potential games. For the SUM-game, we even show that it is not weakly acyclic.
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关键词
Nash Equilibrium, Improve Response, Communication Distance, Private Cost, Potential Game
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