关键词: 三方博弈, 演化博弈, 稳定性, ESS, 线性策略收敛

Abstract: In view of the insufficient stability research of the current tripartite evolutionary game, a generalized three-dimensional dynamic system is constructed by using the replication dynamic equation. Firstly, the evolution trend of the single-group strategy is discussed, and then the system is analyzed according to the Lyapunov stability theory. With the gradual stability and combination of the evolutionary trend of single-group strategies we have made an in-depth study of system stability. The research shows that the strict pure strategy Nash equilibrium is ESS, the non-strict pure strategy Nash equilibrium is linear strategy convergence (custom concept), and all types of hybrid strategy Nash equilibrium are saddle points, which jointly divides the attraction domain of ESS and proves zero. The eigenvalue non-ESS theorem and the ESS non-co-edge theorem, on this basis, give the most number of ESS in the N-dimensional dual-strategy system. Finally, and six sets of classical examples are designed. Firstly, the examples are analyzed with the research results. Then the system simulation is carried out on the examples. The simulation results are consistent with the theoretical analysis, which provides reference and inspiration for the further study of evolutionary games.

Key words: tripartite game, evolutionary game, stability, ESS, linear strategy convergence