Modeling noisy feedback in decentralized self-configuring networks

This paper introduces a generalization of the notion of Nash equilibrium (NE), namely quantal response equilibrium (QRE) in the context of wireless communications. In the QRE, radio devices choose their transmit/receive configuration taking into account that the estimation of their own performance contains a noise component. Here, it is shown that the notion of QRE neatly models decentralized self-configuring networks (DCSN) where feedback messages are impaired by quantization noise or decoding errors. The main contribution of the paper is twofold. First, we show that under the presence of noise in the estimation expected utility, the notion of NE no longer holds, as players cannot be considered rational. Second, we introduce a learning technique that converges to a QRE in a fully decentralized fashion. We present numerical results in the context of a channel selection problem in a parallel multiple access channel in order to illustrate our theoretical results.