Network Resource Allocation: Secrecy Games and Mechanisms with Limited Information Exchange

GE, HAO

doi:https://doi.org/10.21985/n2-yyvb-k015

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Network Resource Allocation: Secrecy Games and Mechanisms with Limited Information Exchange

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We start from a set of users communicating over a Gaussian multiple access wire-tap channel with confidential messages, where users attempt to transmit private messages to a legitimate receiver in the presence of an eavesdropper. While prior work focused on the case where the users were cooperative, we assume that each user is selfish and and so are modeled as playing a non-cooperative game. We assume all users transmits using a superposition coding scheme and give a characterization of the achievable rate region defined by Tekin and Yener using polymatroid properties. One important observation we find is that given a secrecy rate allocation on the dominant face of the achievable rate region, all users have no incentive to deviate. Next we consider maximizing the social welfare, i.e., how can we design a mechanism to find the optimal or close to optimal rate allocation. Traditional network resource allocation mechanisms such as the Kelly mechanism, the second price auction and the VCG mechanism works well for a small scale of network, but two problems arise when the system becomes large: the potential efficiency loss and the communication cost. The VCG mechanism addresses the efficiency loss, but can incur a high communication cost. Namely, the efficiency is addresses by ensure that it is a dominant strategy from agents to truthfully report their utility. Approaches have been studied that relax the communication requirements while also relaxing the incentive guarantees to use Nash equilibria instead of dominant strategies. Here, we take a different approach, and study mechanisms with limited information exchange that still have dominant strategy outcomes, but suffer an acceptable efficiency loss. The basic idea is quantization, we quantize the resource and hence discretize the allocation. We start from a single link resource and propose a quantized VCG mechanism in which information is limited by quantizing the resource into a finite number of units and allocating each of these to one agent via a VCG mechanism. This limits each agent to submitting a finite number of real values. We subsequently consider the case where the feasible region is a polymatroid as in the achievable secrecy rate region. We then show how to use the quantized VCG mechanism to allocate the secure rates. To understand the impact of quantization over performance, we characterize the worst case efficiency in different scenarios and discuss the impact of parameters on the final performance.

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