We propose a general framework to analyze incentives for user cooperation, and characterize the tradeoff between fairness and efficiency for cooperative networks. More specifically, we define the incentive region as a set of action profiles that provides cooperation benefits to all users and focus on the optimization of efficiency and fairness within this region. We introduce a linear resource allocation (LRA) scheme and show that most existing fairness measures can be converted to LRA with different linear coefficient vectors. We then propose the concept of strong price of fairness (SPoF) to study the network efficiency of the strong equilibrium. We show that both the SPoF and fairness measures are connected to the linear coefficient vector of LRA, which makes it possible to study the fairness and efficiency relationship. We then use the random access (RA) system as an example to show how to use the proposed framework to study a specific wireless network.
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