We study game-theoretic mechanisms for routing in ad-hoc networks. Game-theoretic mechanisms capture the non-cooperative and selfish behavior of nodes in a resource-constrained environment. There have been some recent proposals to use incentive-based mechanisms (in particular, VCG) for routing in wireless ad-hoc networks, and some frugality bounds are known when the connectivity graph is essentially complete. We show frugality bounds for random geometric graphs, a well-known model for ad-hoc wireless connectivity. Our main result demonstrates that VCG-based routing in ad-hoc networks exhibits small frugality ratio (i.e., overpayment) with high probability. In addition, we study a more realistic generalization where sets of agents can form
to maximize total profit. We also analyze the performance of VCG under such a community model and show similar bounds. While some recent truthful protocols for the traditional (individual) agent model have improved upon the frugality of VCG by selecting paths to minimize not only the cost but the overpayment, we show that extending such protocols to the community model requires solving NP-complete problems which are provably hard to approximate.
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