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As wireless systems evolve with new mobile technologies, they tend to become complicated in terms of architectures and managements. Auction theory, as a subfield of economics and business management, has been introduced to provide an interdisciplinary technology for radio resource allocation (e.g., subchannels, time slots, and transmit power levels) in the wireless systems. By using various auction approaches, such radio resources are efficiently allocated among users and providers of services in the systems. Participants (i.e., users and providers) of an auction have their own strategies that follow the incentives and rules brought by the auction. Auction methods are widely employed in areas such as cognitive radio, cellular networks, and wireless mesh networks. This paper gives a comprehensive survey of recent auction approaches (i.e., auction-based applications and mechanisms) applied in wireless and …