Exploitation or mercy? Exploring two defection behaviors in donation games

Incorporating strategy complexity into the fundamental dynamics of cooperation and defection presents an avenue for addressing social dilemmas. Based on the donation game, this paper further divides the defectors into hawk-type (\(HD\)) and dove-type defectors (\(DD\)), establishes a three-party game model, and uses evolutionary game theory to study the effects of various factors on cooperation and the stable state that the system ultimately reaches. We discover that in a well-mixed population, the system has the following two stable states: full dove-type defection and three strategies coexist. Additionally, the system also achieves a stable coexistence of cooperators and dove-type defectors in a structured population. The simulation results reveal that lower cooperation cost and higher conflict loss are more conducive to the survival of cooperators, while moderate cooperation benefit can better promote cooperation in the population. Furthermore, the three-strategy game model that distinguishes between hawk-type and dove-type defectors effectively promotes cooperative behavior within the population and maintains population diversity.