Hierarchical Network Formation Games in the Uplink of Multi-Hop Wireless Networks

In this paper, we propose a game theoretic approach to tackle the problem of the distributed formation of the hierarchical network architecture that connects the nodes in the uplink of a wireless multi-hop network. Unlike existing literature which focused on the performance assessment of hierarchical multi-hop networks given an existing topology, this paper investigates the problem of the formation of this topology among a number of nodes that seek to send data in the uplink to a central base station through multi-hop. We model the problem as a hierarchical network formation game and we divide the network into different hierarchy levels, whereby the nodes belonging to the same level engage in a non-cooperative Nash game for selecting their next hop. As a solution to the game, we propose a novel equilibrium concept, the hierarchical Nash equilibrium, for a sequence of multi-stage Nash games, which can be found by backward induction analytically. For finding this equilibrium, we propose a distributed myopic dynamics algorithm, based on fictitious play, in which each node computes the mixed strategies that maximize its utility which represents the probability of successful transmission over the multi-hop communication path in the presence of interference. Simulation results show that the proposed algorithm presents significant gains in terms of average achieved expected utility per user up to 125.6% relative to a nearest neighbor algorithm.