In order to optimize the executing performance of applications and improve the resource utilization efficiency of a system, this paper deals with the resource mapping in grid environments and proposes a novel optimization strategy based on the sequential game. In this strategy, a balanced idea is used to divide the mapping process into two stages, namely the activity distribution and the processor allocation, and an optimal solution is obtained after a limited stage gaming. Moreover, trust degree, an important parameter to measure the executing performance of applications, is dealt with, and the corresponding calculating method is presented. Experimental results indicate that, as compared with the Min-Min strategy, the proposed optimal strategy is of lower time complexity, better executing performance of applications and higher resource utilization efficiency.