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Distributed quality of service support in wireless networks that are sharing unlicensed frequency bands is an increasingly significant research problem. The spectral coexistence of dissimilar radio systems has to be addressed in the near future in concerning the widely deployed IEEE 802.11 wireless local area networks and other future radio systems operating in unlicensed or opportunistically used frequency bands. The competition between independent wireless networks for allocating a common shared radio channel is modeled in this article as a stage-based game model: players, representing wireless networks, interact repeatedly in radio resource sharing games, without direct coordination or information exchange. Solution concepts derived from game theory allow the analysis of such models under the microeconomic aspects of welfare. Decisions players repeatedly have to make are about when and how often to attempt medium access. In multistage games the players apply strategies in order to maximize their observed utility as a summarizing value for successfully supported quality of service. Strategies determine whether competing radio networks cooperate or ignore the presence of other radio networks. The traffic requirements of a player thereby decide which strategy is adequate to guarantee quality of service.