Typical characteristics of remote sensing applications are concurrent tasks, such as those found in disaster rapid response. The existing composition approach to geographical information processing service chain, searches for an optimisation solution and is what can be deemed a "selfish" way. This way leads to problems of conflict amongst concurrent tasks and decreases the performance of all service chains. In this study, a non-cooperative game-based mathematical model to analyse the competitive relationships between tasks, is proposed. A best response function is used, to assure each task maintains utility optimisation by considering composition strategies of other tasks and quantifying conflicts between tasks. Based on this, an iterative algorithm that converges to Nash equilibrium is presented, the aim being to provide good convergence and maximise the utilisation of all tasks under concurrent task conditions. Theoretical analyses and experiments showed that the newly proposed method, when compared to existing service composition methods, has better practical utility in all tasks.