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This paper analyzes distributed asynchronous power and rate control for wireless ad hoc networks. Importantly, all network transmitters are considered to be independent of any management infrastructure and to have the freedom to choose their own arbitrary control rules, using as input only information on local interference and achieved carrier signal-to-interference ratio (CIR). Such an approach respects diverse user preferences of on quality of service (QoS) and allows them to adapt to local network conditions in contrast with conventional cellular systems, whose users must follow centralized control commands from serving base stations. For this purpose, we develop a general non-cooperative game-theoretic framework and characterize the resulting power and rate allocation dynamics in terms of its convergence to network-wide acceptable equilibrium states under stochastic communication channels. Chief among the attractive features of our proposed framework is the fact that it is developed in an entirely abstract way without any particular technological or architectural assumptions, which are typically made in related works. Numerical simulations prove the potential of our approach to provide for fair, robust and comparably better CIR allocation in ad hoc networks with varying topology and user density.