Display omitted •Analyzing intellectual property cooperation mechanism among heterogeneous entities.•GIUR intellectual property cooperation under two types of scenarios is introduced.•Evolutionary game modeling of GIUR intellectual property cooperation is proposed.•Giving the simulation results of GIUR intellectual property cooperation behavior. Intellectual property cooperation is vital to integrating innovation resources, improving innovation energy. It involves many factors including behavioral agents and national economy-macro-management scenarios, should be seriously considered by multi-stakeholders during the process of intellectual property cooperation. Based on the evolutionary game theory, this paper analyzes the Government-Industry-University-Research (GIUR) intellectual property cooperation behavior and its influencing factors from market mechanism and administrative supervision mechanism. Firstly, the newly proposed game models are developed to observe the cooperation behavior which can be realized as strategies and payoff functions of the multi-stakeholders, then, the evolutionary replication dynamics equations are formulated to study evolutionarily stable strategies of multi-stakeholders. Finally, to verify the theoretical results, simulation experiments are conducted with meaningful results: under the market mechanism, the reasonable government subsidy incentive, and the liquidated damages can make GIUR practice an active intellectual property cooperation behavior to each other; under the administrative supervision mechanism, reasonable tax rate and administrative penalties are conducive to promoting and stabilizing GIUR intellectual property cooperation. In addition, the government will have the “interest appeal” to maximize additional social benefits in the game with enterprises, universities or research institutes. The results can guide GIUR to make better decisions in the future.