A further analysis of the role of heterogeneity in coevolutionary spatial games

Abstract

Heterogeneity has been studied as one of the most common explanations of the puzzle of cooperation in social dilemmas. A large number of papers have been published discussing the effects of increasing heterogeneity in structured populations of agents, where it has been established that heterogeneity may favour cooperative behaviour if it supports agents to locally coordinate their strategies. In this paper, assuming an existing model of a heterogeneous weighted network, we aim to further this analysis by exploring the relationship (if any) between heterogeneity and cooperation. We adopt a weighted network which is fully populated by agents playing both the Prisoner's Dilemma or the Optional Prisoner's Dilemma games with coevolutionary rules, i.e., not only the strategies but also the link weights evolve over time. Surprisingly, results show that the heterogeneity of link weights (states) on their own does not always promote cooperation; rather cooperation is actually favoured by the increase in the number of overlapping states and not by the heterogeneity itself. We believe that these results can guide further research towards a more accurate analysis of the role of heterogeneity in social dilemmas.

Mobility restores the mechanism which supports cooperation in the voluntary prisoner’s dilemma game

“…Besides, results show that when the agents are allowed to abstain, the population of mobile agents will never converge to full defection. Finally, it is noteworthy that results also echo the findings of previous research concerning the PD and VPD games on weighted networks [48,50,51], i.e. a coevolutionary model in which the link weights are also subject to evolution.…”

“…Despite the very recent introduction of the VPD game in a diluted network with a purely random mobility scenario [47], many questions regarding the impact of mobility, in both the sustenance of biodiversity and the potential for widespread cooperation, remain unanswered. For instance, given the recent advances in the understanding of coevolutionary models [48][49][50][51][52][53][54], what happens to the population when considering agent mobility in a coevolutionary fashion? Thus, without loss of generality, this research introduces the VPD game with a coevolutionary model where not only the agents' strategies but also their movement is subject to the evolutionary process, which provides a more realistic representation of mobility within the domain of voluntary/optional participation.…”

Cooperation in the spatial prisoner’s dilemma game with probabilistic abstention

“…Given the nature of the classic PD and OPD games, it is known that in a well-mixed population, defection and abstention are usually the dominant strategies respectively. As discussed in previous work 22,63 , this happens because cooperators need to form clusters to be able to protect themselves against exploitation from defectors, and if we consider a randomly initialized population, it takes a few steps for cooperators to cluster. Meanwhile, the defection rate increases quickly in the initial steps until the agents reach a stage where defectors have more chance of finding another defector than a cooperator.…”

Evoplex: A platform for agent-based modeling on networks

“…We provide a few examples of plugins of easy reuse and customization. 1 In summary, a plugin comprises four files: CMakeLists.txt which does not need to be changed by the modeler and is just a CMake script to ease the compilation process and make it portable across different compilers and IDEs, the plugin.cpp (source) and plugin.h (header) files where the modeler implements the model's algorithm, and metadata.json which holds the definition of all the attributes of the model. Moreover, Evoplex uses automated Continuous Integration (CI) to make sure that the code base works as expected and to allow early detection of problems.…”

“…Evoplex is intended to address research whose methodology comprises a simulation-based approach to evolve outcomes of populations of autonomous and interacting agents. It has been used to support research in a number of areas, including spatial game theory and evolutionary game theory [1,23,24]. In those scenarios, agents are described in terms of graph theory, i.e., a graph (network) consisting of a set of nodes (agents) and edges (agents' connections).…”