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In ad hoc networks, reducing energy consumption and improving throughput are both important for high network performance. This paper presents a joint power and rate control adaptive algorithm to optimize the trade-off between power consumption and throughput in ad hoc networks. Each node chooses its own transmission power and rate based on limited environment information in order to achieve optimal transmission efficiency. In a fictitious game framework with strategy space transformation, our joint power and rate control adaptive algorithm can be viewed as a supermodular game. By interpreting the supermodular game using myopic best response updates, this algorithm can converge to the unique optimal transmission efficiency. Finally, the simulation results show that this supermodular game approach improves the average transmission efficiency by about 33%.