We consider multiprocessor system-on-chip (MP-SoC) integrating several processing elements (PE). These architectures require distributed and scalable control techniques for run-time optimization of applicative parameters. Our approach is to use the game theory as an optimization model to solve the trade-off issues at run-time. We applied it to the distributed dynamic voltage frequency scaling (DVFS) management, adjusting at run-time the frequency set of each PE based on the synchronization between tasks of the application graph and the PE temperature profile. Results show that the analyzed algorithm converges to a solution in about 94% of the cases and in less than 40 calculation cycles for a 100-processor MP-SoC. It reaches an average optimization of 89% compared to an off-line centralized reference but about 140 times faster when simulating.