Conformity enhances network reciprocity in evolutionary social dilemmas

Abstract

The pursuit of highest payoffs in evolutionary social dilemmas is risky and sometimes inferior to conformity. Choosing the most common strategy within the interaction range is safer because it ensures that the payoff of an individual will not be much lower than average. Herding instincts and crowd behaviour in humans and social animals also compel to conformity in their own right. Motivated by these facts, we here study the impact of conformity on the evolution of cooperation in social dilemmas. We show that an appropriate fraction of conformists within the population introduces an effective surface tension around cooperative clusters and ensures smooth interfaces between different strategy domains. Payoff-driven players brake the symmetry in favour of cooperation and enable an expansion of clusters past the boundaries imposed by traditional network reciprocity. This mechanism works even under the most testing conditions, and it is robust against variations of the interaction network as long as degree-normalized payoffs are applied. Conformity may thus be beneficial for the resolution of social dilemmas.

Keywords: conformity; cooperation; evolutionary games; network reciprocity; social dilemmas.

Figure 1.

Evolution of cooperation in the weak Prisoner's Dilemma with conformity-driven players, as obtained on the square lattice in dependence on the temptation to defect T and the density of conformists ρ. The colour map encodes the stationary fraction of cooperators f_C. While, expectedly, f_C decreases with increasing T values, it can also be observed that the dependence of f_C on ρ is non-monotonous, especially for intermediate values of T. The bell-shaped outlay of f_C on ρ is owing to conformity-enhanced network reciprocity as ρ > 0 on the one hand, and the strategy-neutral relation of conformists in the absence of payoff-driven players at ρ = 1 on the other hand. (Online version in colour.)

Figure 2.

Evolution of cooperation from a random initial state under the influence of conformity. Depicted are characteristic spatial patterns, as obtained with the weak Prisoner's Dilemma game on a square lattice using T = 1.45 and ρ = 0.81. Payoff-driven cooperators (defectors) are depicted dark blue (dark red), while conformity-driven cooperators (defectors) are depicted bright blue (pale red). Starting from a random initial state (a), conformity-driven players introduce spontaneous flocking of cooperators into compact clusters with smooth interfaces separating them from defectors (b). Payoff-driven players subsequently reveal the long-term benefits of cooperation and the cluster grows, all the while maintaining surface tension and thus a smooth interface (c). The effectiveness of this conformity-enhanced network reciprocity eventually propels cooperators to near-complete dominance (d). For clarity, we have here used a small square lattice with linear size L = 100. (Online version in colour.)

Figure 3.

The inset features a schematic presentation of two typical interfaces that separate competing domains when payoff-driven players (dark colours) are rare. In the complete absence of such players, conformity-driven players (pale colours) would build perfectly smooth (straight) interfaces. In their presence, however, the interfaces might be modified by the most likely elementary steps, which are marked in the figure as follows: those conformity-driven players who are at the edge of a moving interface (marked by tilted-line boxes) can change their strategy with probability 1/2, whereas payoff-driven players are most likely to imitate a strategy along the direction of white arrows. These elementary steps determine the leading terms in equation (2.3). Main panel shows the time derivative of the fraction of cooperators density in dependence on T, according to equation (2.3), that is due solely to the above-mentioned elementary processes. It can be observed that only for T > 1.25 the tide shifts in favour defectors. (Online version in colour.)

Figure 4.

Evolution of cooperation in the donation game (true Prisoner's Dilemma) with conformity-driven players, as obtained on the square lattice in dependence on the temptation to defect T and the density of conformists ρ. The colour map encodes the stationary fraction of cooperators f_C. Results are qualitatively similar to those presented in figure 1 for the weak Prisoner's Dilemma game, thereby confirming the robustness of the enhanced network reciprocity to variations in the contested social dilemma. It is also worth noting that network reciprocity alone is practically unable to sustain cooperation in the donation game if T > 1, which indicates that the identified conformity-enhanced network reciprocity works well even under the most testing conditions. (Online version in colour.)

Figure 5.

Evolution of cooperation in the weak Prisoner's Dilemma with conformity-driven players, as obtained on the scale-free network in dependence on the temptation to defect T and the density of conformists ρ. The colour map encodes the stationary fraction of cooperators f_C. The change in the topology of the interaction network also leaves the results qualitatively unaffected, thus further corroborating the robustness of the identified conformity-enhanced network reciprocity. Importantly, we have here applied degree-normalized payoffs. If absolute payoffs are applied on strongly heterogeneous networks, then the heterogeneity alone provides the maximal support to network reciprocity, and hence the impact of conformity is either negligible or even slightly negative (not shown). (Online version in colour.)