Collective navigation of complex networks: Participatory greedy routing

Many networks are used to transfer information or goods, in other words, they are navigated. The larger the network, the more difficult it is to navigate efficiently. Indeed, information routing in the Internet faces serious scalability problems due to its rapid growth, recently accelerated by the rise of the Internet of Things. Large networks like the Internet can be navigated efficiently if nodes, or agents, actively forward information based on hidden maps underlying these systems. However, in reality most agents will deny to forward messages, which has a cost, and navigation is impossible. Can we design appropriate incentives that lead to participation and global navigability? Here, we present an evolutionary game where agents share the value generated by successful delivery of information or goods. We show that global navigability can emerge, but its complete breakdown is possible as well. Furthermore, we show that the system tends to self-organize into local clusters of agents who participate in the navigation. This organizational principle can be exploited to favor the emergence of global navigability in the system.Comment: Supplementary Information and Videos: https://koljakleineberg.wordpress.com/2016/11/14/collective-navigation-of-complex-networks-participatory-greedy-routing

Prisoner's dilemma in structured scale-free networks

The conventional wisdom is that scale-free networks are prone to cooperation spreading. In this paper we investigate the cooperative behaviors on the structured scale-free network. On the contrary of the conventional wisdom that scale-free networks are prone to cooperation spreading, the evolution of cooperation is inhibited on the structured scale-free network while performing the prisoner's dilemma (PD) game. Firstly, we demonstrate that neither the scale-free property nor the high clustering coefficient is responsible for the inhibition of cooperation spreading on the structured scale-free network. Then we provide one heuristic method to argue that the lack of age correlations and its associated `large-world' behavior in the structured scale-free network inhibit the spread of cooperation. The findings may help enlighten further studies on evolutionary dynamics of the PD game in scale-free networks.Comment: Definitive version accepted for publication in Journal of Physics

Mutual Trust and Cooperation in the Evolutionary Hawks-Doves Game

Using a new dynamical network model of society in which pairwise interactions are weighted according to mutual satisfaction, we show that cooperation is the norm in the Hawks-Doves game when individuals are allowed to break ties with undesirable neighbors and to make new acquaintances in their extended neighborhood. Moreover, cooperation is robust with respect to rather strong strategy perturbations. We also discuss the empirical structure of the emerging networks, and the reasons that allow cooperators to thrive in the population. Given the metaphorical importance of this game for social interaction, this is an encouraging positive result as standard theory for large mixing populations prescribes that a certain fraction of defectors must always exist at equilibrium.Comment: 23 pages 12 images, to appea

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Symbiotic Cell Differentiation and Cooperative Growth in Multicellular Aggregates

As cells grow and divide under a given environment, they become crowded and resources are limited, as seen in bacterial biofilms and multicellular aggregates. These cells often show strong interactions through exchanging chemicals, as in quorum sensing, to achieve mutualism. Here, to achieve stable division of labor, three properties are required. First, isogenous cells differentiate into several types. Second, this aggregate of distinct cell types shows better growth than that of isolated cells, by achieving division of labor. Third, this cell aggregate is robust in the number distribution of differentiated cell types. We here address how cells acquire the ability of cell differentiation and division of labor simultaneously, which is also connected with the robustness of a cell society. For this purpose, we developed a dynamical-systems model of cells consisting of chemical components with intracellular catalytic reaction dynamics. The reactions convert external nutrients into internal components for cellular growth, and the divided cells interact via chemical diffusion. We found that cells sharing an identical catalytic network spontaneously differentiate via induction from cell-cell interactions, and then achieve division of labor, enabling a higher growth rate than that in the unicellular case. This symbiotic differentiation emerged for a class of reaction networks with limited resources and strong cell-cell interactions. Then, robustness in the cell type distribution was achieved, while instability of collective growth could emerge even among the cooperative cells when the internal reserves of products were dominant. The present mechanism is simple and general as a natural result of interacting cells with resource limitation, and is consistent with the observed behaviors and forms of several aggregates of unicellular organisms.Comment: 14 pages, 6 figure