Seasonal payoff variations and the evolution of cooperation in social dilemmas

Abstract

Varying environmental conditions affect relations between interacting individuals in social dilemmas, thus affecting also the evolution of cooperation. Oftentimes these environmental variations are seasonal and can therefore be mathematically described as periodic changes. Accordingly, we here study how periodic shifts between different manifestations of social dilemmas affect cooperation. We observe a non-trivial interplay between the inherent spatiotemporal dynamics that characterizes the spreading of cooperation in a particular social dilemma type and the frequency of payoff changes. In particular, we show that periodic changes between two available games with global ordering best be fast, while periodic changes between global and local ordering games best be slow for cooperation to thrive. We also show that the frequency of periodic changes between two local ordering social dilemmas is irrelevant, because then the process is fast and simply the average cooperation level of the two is returned. The structure of the interaction network plays an important role too in that lattices promote local ordering, whilst random graphs hinder the formation of compact cooperative clusters. Conversely, for local ordering the regular structure of the interaction network is only marginally relevant as role-separating checkerboard patterns do not rely on long-range order.

Blocking defector invasion by focusing on the most successful partner

“…It is worth noting that the reported cooperator supporting mechanism fits nicely to those observations where the introduced strategy-neutral rule has biased impact on the strategy invasion of competing strategies [44,45,46,47,48,49]. Hence these mechanisms provide an alternative way to understand to original enigma and explain why cooperation may prevail among selfish agents.…”

Cooperation and competition between pair and multi-player social games in spatial populations

“…We note that the simultaneous usage of different games was already used by some previous works 47 , 48 . But in these cases the application of diverse payoff elements was a predefined microscopic rule which was assigned to specific players or the usage of alternative payoff elements were the subject of a time-course 49 – 53 . In our present case, however, the application of different payoff elements is the consequence of a natural evolutionary process which is driven by an individual imitation procedure.…”

Strategy equilibrium in dilemma games with off-diagonal payoff perturbations

“…In EGT, heterogeneity can be related to different aspects of a game, e.g., incentives, interaction topology, learning rates, and dynamics. Previous investigations, such as [22,29,[33][34][35][36][37][38], showed that heterogeneity can support cooperative behaviors in many competitive scenarios. At the same time, other studies such as [39] reported that heterogeneous networks do not promote cooperation when humans play the prisoner's dilemma.…”

“…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.…”

“…We deem it relevant to mention previous seminal works, such as [55][56][57][58][59], that (to the best of our knowledge) first studied such disorder in EGT. More recently, the effect of payoff noise on phase transitions has been the core of much research that has shed light on how different types of perturbations can lead to the emergence of cooperation [8,27,33,52,53,[60][61][62][63][64][65][66]. So, here, starting from the model proposed in [8], which introduces payoff perturbation in the context of the imitation update rule for all payoff entries, we perform a full analysis under different settings, and then we study the microscopical mechanism that leads to the observed macroscopic results.…”