The knowledge-based competition between agents in an innovation ecosystem not only impacts the survival and development of individuals but also affects the evolution of the innovation ecosystem. From the evolutionary game perspective, this paper explores agents’ choice of appropriability strategies and following strategies in an innovation ecosystem under different environments. An asymmetric evolutionary game model and a multi-agent simulation model are constructed successively to analyze the influence of institutional, ecological, and technological factors on the evolutionary equilibrium stability and evolutionary stable strategies of an innovation ecosystem. It is found that the key factors affecting the equilibrium of system evolution are costs of patent operation and protection, the degree of relief on patent disputes, government subsidies, and the relative technical difficulty between substitution and imitation. Based on different situations formed by the above factors, there are four evolutionary stable states: (patenting, imitation), (patenting, substitution), (secret, imitation), and continuous fluctuation of strategies. The outcomes of simulation models which show random fluctuation are consistent with the results of evolutionary stability analysis in the trend. When a cooperation network is dense or a search scope is wide, the long-term evolution of each group tends to the strategies with large average income expectation due to the increase of interaction, the decrease of decision uncertainty, and the improvement of decision effectiveness. When information fuzziness is high, the uncertainty of decision-making increases, and the system fluctuates more violently. Moreover, the strategic interaction between groups is weakened. The long-term evolution of the system deviates from the results of evolutionary stability analysis.