Under the background of information asymmetry and conflict goals between high education institutions management (taking budget allocation and performance management role) and teachers (taking budget execution role), this paper applies multi-task and multi-agent principal-agent paradigm along with the auction model, to build a model of performance based budgeting management system for high education institutions. Through the theoretical analyses of the model, this paper obtains theoretical relationships among states of budgeting system. Key relationships include the teachers' behavior and incentive coefficients, optimal allocation of resources, optimal incentive setting for teachers and intra-resource transfer pricing. Finally, this paper applies the model to the analysis of the allocation of graduate training funds and teacher salary budgets in University A. University A invests training funds to recruit graduate students, allocates graduate students and designs teacher incentive mechanism for the teaching and research outputs to achieve performance goals. The application demonstrates that University A can optimally adjust its incentive system and output targets to alleviate the dispute on the graduate research assistant fee while achieving its goals. The results of this paper provide a theoretical guidance for high education institutions to improve the performance based budgeting system and the efficiency of resource allocation and school running.