Identification of influential invaders in evolutionary populations

Abstract

The identification of the most influential nodes has been a vibrant subject of research across the whole of network science. Here we map this problem to structured evolutionary populations, where strategies and the interaction network are both subject to change over time based on social inheritance. We study cooperative communities, which cheaters can invade because they avoid the cost of contributions that are associated with cooperation. The question that we seek to answer is at which nodes cheaters invade most successfully. We propose the weighted degree decomposition to identify and rank the most influential invaders. More specifically, we distinguish two kinds of ranking based on the weighted degree decomposition. We show that a ranking strategy based on negative-weighted degree allows to successfully identify the most influential invaders in the case of weak selection, while a ranking strategy based on positive-weighted degree performs better when the selection is strong. Our research thus reveals how to identify the most influential invaders based on statistical measures in dynamically evolving cooperative communities.

Ranking the invasions of cheaters in structured populations

“…The weighted degree decomposition (WDD) is defined in 36 as a way to compute the importance of nodes by considering the difference between the removed nodes and the remaining nodes. In general, two types of nodes will be in the network according to the weighted degree decomposition method, and they are defined to be seed nodes and potential nodes.…”

“…• k-shell ranking: the top-n nodes are selected to be defectors based on their k-shell 11 (higher the k-shell of a node, higher the chances that the node is selected). • N-weighted degree ranking: the top-n nodes are selected to be defectors based on the negative weighted degree 36 . • P-weighted degree ranking: the top-n nodes are selected to be defectors based on the positive weighted degree 36 .…”

“…• N-weighted degree ranking: the top-n nodes are selected to be defectors based on the negative weighted degree 36 . • P-weighted degree ranking: the top-n nodes are selected to be defectors based on the positive weighted degree 36 .…”

Ranking game on networks: The evolution of hierarchical society

“…In turn, the evolving environment drives individuals to adapt to the surroundings. In the context of a network environment, evolutionary game theory is married with social network theory, which has recently provided insight into agent-action-network evolutions [11][12][13][14][15][16][17]. In this series of studies on spatial evolutionary games, a variety of games have been tested on social networks, including prisoner's dilemma (PD) [18][19][20][21][22][23], snowdrift [24], public goods [25], and minority games [26][27][28].…”

“…The dynamics of influence was investigated in hierarchical populations [5]. In another study, influential invaders were identified in a structured evolutionary population [17]. Most models for evolutionary games on networks simply consider a single network.…”