What are the most effective strategies for optimizing graphical performance and battery efficiency in mobile games targeting budget devices? Specifically, considering the constraints imposed by mid-range hardware, which techniques have proven successful in maintaining a stable frame rate while minimizing power consumption? For example, what role do dynamic resolution scaling, selective post-processing, and adaptive quality adjustments play in achieving an acceptable balance between visual fidelity and performance? Are there trade-offs or benchmarks available that provide comparative insights into different optimization approaches on lower-end mobile hardware? Input based on empirical evidence or technical case studies would be highly appreciated.