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This paper investigates the properties of social choice functions, that represent resource allocation strategies in interference coupled wireless systems. The resources can be physical layer parameters such as power vectors or antenna weights. The paper investigates the permissible social choice functions, which can be implemented by a mechanism in either Nash equilibria or dominant strategy - for utility functions representing interference coupled wireless systems. Strategy proofness and efficiency properties of social choice functions are used to capture the properties of non-manipulability and Pareto optimality of solution outcomes of resource allocation strategies, respectively. The analysis indicates certain inherent limitations when designing strategy proof and efficient resource allocation strategies. These restrictions are investigated in an analytical mechanism design framework of interference coupled wireless systems. Furthermore, the paper characterizes the Pareto optimal boundary points (efficient) of utility sets of interference coupled wireless system. An axiomatic framework of interference functions is used to capture interference coupling. The Pareto optimal boundary points for the cases of individual power constraints and a total power constraint are described based on the properties of the underlying interference functions.