Stability analysis for replicator dynamics of evolutionary snowdrift games

Stability analysis is presented in this paper to study the evolution of large populations of well mixed individuals playing three typical reactive strategies - always cooperate, tit-for-tat and suspicious tit-for-tat. After parameterizing the corresponding payoff matrices, we use replicator dynamics, a powerful tool from evolutionary game theory, to investigate how population dynamics evolve over time. We show the corresponding equilibria as well as their stability properties change as the payoff for mutual cooperation changes. Both theoretical analysis and simulation study are provided, which complements and further develops some existing results in theoretical biology and sociology.