Joint Random Access and Power Control Game in Ad Hoc Networks with Noncooperative Users Chengnian Long and Xinping Guan Department of Automation School of Electronic, Information and Electrical Engineering Shanghai Jiaotong University, Shanghai, China longcn@sjtu.edu.cn Abstract. We consider a distributed joint random access and power control scheme for interference management in wireless ad hoc networks. To derive decentralized solutions that do not require any cooperation among the users, we formulate this problem as non-cooperative joint random access and power control game, in which each user minimizes its average transmission cost with a given rate constraint. Using super- modular game theory, the existence and uniqueness of Nash equilibrium are established. Furthermore, we present an asynchronous distributed algorithm to compute the solution of the game based on myopic best response updates, which converges to Nash equilibrium globally. Keywords: wireless ad hoc networks, random access, power control, supermodular game, Nash equilibrium. 1 Introduction Since wireless ad hoc networks use a common transmission medium, collision may occur in the presence of simultaneous transmissions by two or more wireless links lying in the interference range of each other. Thus, mitigating interference is a fundamental problem for increasing spectral efficiency in wireless ad hoc net- works. Important mechanisms for interference management in wireless networks are medium access control (MAC) and power control. This is a complex and intriguing problem since the selection of active link and its power level funda- mentally affects many aspects of the operation of the network and its resulting performance; for instance the quality of the signal received at the receiver, the interference it creates for the other receivers and energy consumption at each node. Traditionally, interference management for ad hoc networks is primarily im- plemented at the lower layers independently. In scheduling-based MAC protocols (TDMA), the interference management is implemented by a distributed power control for simultaneous active links in a slot. The scheduling problem is to decide in each time slot which source-destination pairs communicate according to some performance index, e.g., maximizing the number of simultaneous transmissions. The power control and scheduling design is separated. In the contention-based J. Zheng et al. (Eds.): ADHOCNETS 2009, LNICST 28, pp. 679–690, 2010. c  ICST Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering 2010