Global Convergence for Replicator Dynamics of Repeated Snowdrift Games

To understand the emergence and sustainment of cooperative behavior in interacting collectives, we perform global convergence analysis for replicator dynamics a large, well-mixed population individuals playing repeated snowdrift game with four typical strategies, which are always cooperate (ALLC), tit-for-tat (TFT), suspicious (STFT), defect (ALLD). The dynamical model is 3-D ordinary differential equation (ODE) system that parameterized by payoffs base game. Instead routine searches evolutionarily stable strategies sets, expand our to determining asymptotic solution trajectories starting from any initial state, particular, show full range payoffs, every trajectory converges an equilibrium point. What enables us achieve such comprehensive results studying two ratios state variables, each either monotonically increases or decreases half-spaces separated their corresponding planes. highlight findings. First, inclusion TFT- STFT-players, types conditional strategy players game, share cooperators overall compared situation when consists only ALLC ALLD-players. Second, surprisingly enough, regardless there exists set conditions under ALLC-players do not vanish long run, does hold other three players.