Dissimilarity-driven behavior and cooperation in the spatial public goods game

Abstract

In this paper, we explore the impact of four different types of dissimilarity-driven behavior on the evolution of cooperation in the spatial public goods game. While it is commonly assumed that individuals adapt their strategy by imitating one of their more successful neighbors, in reality only very few will be awarded the highest payoffs. Many have equity or equality preferences, and they have to make do with an average or even with a low payoff. To account for this, we divide the population into two categories. One consists of payoff-driven players, while the other consists of dissimilarity-driven players. The later imitate the minority strategy in their group based on four different dissimilarity-driven behaviors. The rule that most effectively promotes cooperation, and this regardless of the multiplication factor of the public goods game, is when individuals adopt the minority strategy only when their payoff is better than that of their neighbors. If the dissimilarity-driven players adopt the minority strategy regardless of the payoffs of others, or if their payoff is the same, the population typically evolves towards a neutral state where cooperators and defectors are equally common. This may be beneficial when the multiplication factor is low, when defectors would otherwise dominate. However, if the dissimilarity-driven players adopt the minority strategy only when their payoff is worse than that of their neighbors, then cooperation is not promoted at all in comparison to the baseline case in the absence of dissimilarity-driven behavior. We explore the pattern formation behind these results, and we discuss their wider implications for the better understanding of cooperative behavior in social groups.

Strategy equilibrium in dilemma games with off-diagonal payoff perturbations

“…Here we consider the usual imitative rule [51], the Ising (or Glauber dynamics) rule [68], and the dynamic win-stay-loseshift (WSLS) rule [69]. This is done so we can study the robustness of the effects created by payoff perturbation, since previous works have extensively shown how the update rules can lead to different behaviors [22,34,35,47,70,71].…”

“…One way to study the influence of such random variations is to represent each different environmental condition as a new factor in the equations of a model. Following this method, many authors have made important advances in the understanding of how a number of conditions can drive the system dynamics, such as resource heterogeneity [46], different behaviors [47,48], seasonal variations [33], diverse learning rates [49], different death rates [50], interaction topologies [51], and so on. However, another way to understand these phenomena is to study the behavior of a population whose evolution can be affected by a payoff matrix constantly perturbed by stochastic noise with zero mean value [52][53][54], regardless of its origin.…”

Acculturation and the evolution of cooperation in spatial public goods games

“…However, if mechanisms like spatial structure are present, cooperators may have a chance depending on the cost to benefit ratio of participating in the PGG [12][13][14][15][16]. Besides spatial structure, that gives rise to network reciprocity, other major mechanisms that help cooperation are the punishment of defectors, the rewarding of cooperators and the ability to not participate in the game [17][18][19][20][21][22][23][24][25][26][27][28]. In spatial PGG, cooperation can thrive if the multiplicative factor is high enough.…”

Strategy equilibrium in dilemma games with off-diagonal payoff perturbations

“…One way to study the influence of such random variations is to represent each different environmental condition as a new factor in the equations of a model. Following this method, many authors have done important advances in the understanding of how a number of conditions can drive the system dynamics, such as resource heterogeneity [40], different behaviours [41,42], seasonal variations [29], diverse learning rates [43], different death rates [44], interaction topologies [45], and so on. However, another way to understand these phenomena is to study the behaviour of a population whose evolution can be affected by a payoff matrix constantly perturbed by stochastic noise with zero mean value [46][47][48], irregardless of its origin.…”