Grid computing employs resource sharing in heterogeneous computing networks to solve complex computing tasks. To provide suitable performance and response times, the available resources have to be scheduled and coordinated for workflow implementation in the grid environment. Therefore, task scheduling and resource allocation are very important to achieve high performance in grid computing. Game theory is one approach which can be used for scheduling. In this paper, a noncooperative game is proposed to minimize the time and cost of scheduling. Moreover, the aim of the proposed approach is to encourage resource brokers to use an optimal scheduling algorithm. In the proposed game, the broker profit is increased when a solution is proposed with lower time and cost for the users.