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Resource price prediction is one of the most important problems in resource scheduling optimization in grid. But price status is difficult to estimate accurately due to the dynamic nature and heterogeneity of grid resource. In response to this issue, a resource scheduling strategy which uses sequential game method to predict resource price for time optimization in a proportional resource sharing environment is proposed. The problem of multiple users bidding to compete for a common computational resource is formulated as a multi-player dynamic game. Through finding the Nash equilibrium solution of the multi-player dynamic game, resource price is predicted. Using this price information, a set of users' optimal bids are produced to partition resource capacity according to proportional sharing mechanism. The experiments are performed based on GridSim toolkits and the results show that the proposed strategy could generate reasonable user bids, reduce resource processing time, hence overcome the deficiency of Bredin's strategy that it doesn't consider resource price variation. Conclusion indicates that employing sequential game method for price prediction is feasible in grid resource scheduling and adapts better to the dynamic nature of heterogeneous resource in grid environment.