8 research outputs found
A generalized public goods game with coupling of individual ability and project benefit
Facing a heavy task, any single person can only make a limited contribution
and team cooperation is needed. As one enjoys the benefit of the public goods,
the potential benefits of the project are not always maximized and may be
partly wasted. By incorporating individual ability and project benefit into the
original public goods game, we study the coupling effect of the four
parameters, the upper limit of individual contribution, the upper limit of
individual benefit, the needed project cost and the upper limit of project
benefit on the evolution of cooperation. Coevolving with the individual-level
group size preferences, an increase in the upper limit of individual benefit
promotes cooperation while an increase in the upper limit of individual
contribution inhibits cooperation. The coupling of the upper limit of
individual contribution and the needed project cost determines the critical
point of the upper limit of project benefit, where the equilibrium frequency of
cooperators reaches its highest level. Above the critical point, an increase in
the upper limit of project benefit inhibits cooperation. The evolution of
cooperation is closely related to the preferred group-size distribution. A
functional relation between the frequency of cooperators and the dominant group
size is found
Synchronization in networks with multiple interaction layers
The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multilayered structure of connections affects the synchronization properties of dynamical systems evolving on top of it is a highly relevant endeavor in mathematics and physics and has potential applications in several socially relevant topics, such as power grid engineering and neural dynamics. We propose a general framework to assess the stability of the synchronized state in networks with multiple interaction layers, deriving a necessary condition that generalizes the master stability function approach. We validate our method by applying it to a network of Rössler oscillators with a double layer of interactions and show that highly rich phenomenology emerges from this. This includes cases where the stability of synchronization can be induced even if both layers would have individually induced unstable synchrony, an effect genuinely arising from the true multilayer structure of the interactions among the units in the network
Rewarding evolutionary fitness with links between populations promotes cooperation
Evolution of cooperation in the prisoner׳s dilemma and the public goods game is studied, where initially players belong to two independent structured populations. Simultaneously with the strategy evolution, players whose current utility exceeds a threshold are rewarded by an external link to a player belonging to the other population. Yet as soon as the utility drops below the threshold, the external link is terminated. The rewarding of current evolutionary fitness thus introduces a time-varying interdependence between the two populations. We show that, regardless of the details of the evolutionary game and the interaction structure, the self-organization of fitness and reward gives rise to distinguished players that act as strong catalysts of cooperative behavior. However, there also exist critical utility thresholds beyond which distinguished players are no longer able to percolate. The interdependence between the two populations then vanishes, and cooperators are forced to rely on traditional network reciprocity alone. We thus demonstrate that a simple strategy-independent form of rewarding may significantly expand the scope of cooperation on structured populations. The formation of links outside the immediate community seems particularly applicable in human societies, where an individual is typically member in many different social networks
Multiplex Decomposition of Non-Markovian Dynamics and the Hidden Layer Reconstruction Problem
Elements composing complex systems usually interact in several different ways
and as such the interaction architecture is well modelled by a multiplex
network. However often this architecture is hidden, as one usually only has
experimental access to an aggregated projection. A fundamental challenge is
thus to determine whether the hidden underlying architecture of complex systems
is better modelled as a single interaction layer or results from the
aggregation and interplay of multiple layers. Here we show that using local
information provided by a random walker navigating the aggregated network one
can decide in a robust way if the underlying structure is a multiplex or not
and, in the former case, to determine the most probable number of hidden
layers. As a byproduct, we show that the mathematical formalism also provides a
principled solution for the optimal decomposition and projection of complex,
non-Markovian dynamics into a Markov switching combination of diffusive modes.
We validate the proposed methodology with numerical simulations of both (i)
random walks navigating hidden multiplex networks (thereby reconstructing the
true hidden architecture) and (ii) Markovian and non-Markovian continuous
stochastic processes (thereby reconstructing an effective multiplex
decomposition where each layer accounts for a different diffusive mode). We
also state and prove two existence theorems guaranteeing that an exact
reconstruction of the dynamics in terms of these hidden jump-Markov models is
always possible for arbitrary finite-order Markovian and fully non-Markovian
processes. Finally, we showcase the applicability of the method to experimental
recordings from (i) the mobility dynamics of human players in an online
multiplayer game and (ii) the dynamics of RNA polymerases at the
single-molecule level.Comment: 40 pages, 24 figure
The structure and dynamics of multilayer networks
In the past years, network theory has successfully characterized the
interaction among the constituents of a variety of complex systems, ranging
from biological to technological, and social systems. However, up until
recently, attention was almost exclusively given to networks in which all
components were treated on equivalent footing, while neglecting all the extra
information about the temporal- or context-related properties of the
interactions under study. Only in the last years, taking advantage of the
enhanced resolution in real data sets, network scientists have directed their
interest to the multiplex character of real-world systems, and explicitly
considered the time-varying and multilayer nature of networks. We offer here a
comprehensive review on both structural and dynamical organization of graphs
made of diverse relationships (layers) between its constituents, and cover
several relevant issues, from a full redefinition of the basic structural
measures, to understanding how the multilayer nature of the network affects
processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201