Evolution of cooperation driven by zealots

Abstract

Recent experimental results with humans involved in social dilemma games suggest that cooperation may be a contagious phenomenon and that the selection pressure operating on evolutionary dynamics (i.e., mimicry) is relatively weak. I propose an evolutionary dynamics model that links these experimental findings and evolution of cooperation. By assuming a small fraction of (imperfect) zealous cooperators, I show that a large fraction of cooperation emerges in evolutionary dynamics of social dilemma games. Even if defection is more lucrative than cooperation for most individuals, they often mimic cooperation of fellows unless the selection pressure is very strong. Then, zealous cooperators can transform the population to be even fully cooperative under standard evolutionary dynamics.

Figure 1. Fraction of cooperators among the ordinary players in the presence of perfectly zealous cooperators (i.e., p = 1).

The lines represent T = 1 + y/w. I used a typical payoff matrix of the prisoner's dilemma game given by R = 1, T > 1, and S = P = 0. I set (a) w = 0.1 and (b) w = 1.

Figure 2. Fraction of cooperators among the ordinary players as a function of the additional density of zealous players (i.e., y) and the probability of unconditional cooperation for zealous players (i.e., p).

I set R = 1 and S = P = 0. (a) w = 0.1, T = 1.5. (b) w = 0.1, T = 2.5. (c) w = 1, T = 1.5. (d) w = 1, T = 2.5.

Figure 3. Fraction of cooperators among the ordinary players in the prisoner's dilemma game when the pairwise comparison rule is used for the updating.

I set R = 1, S = P = 0, and . (a) T = 1.5. (b) T = 2.5.

Figure 4. Fraction of cooperators among the ordinary players as a function of the temptation payoff (i.e., T ).

I set R = 1 and S = P = 0. (a) w = 0.1. (b) w = 1.

Figure 5. Fraction of cooperators among the ordinary players as a function of y and p in the snowdrift game.

I set R = β − 0.5, S = β − 1, T = β, P = 0, and β = 0.5. (a) w = 0.1. (b) w = 1.