Short versus long term benefits and the evolution of cooperation in the prisoner's dilemma game

In this paper I investigate the evolution of cooperation in the prisoner's dilemma when individuals change their strategies subject to performance evaluation of their neighbours over variable time horizons. In the monochrome setting, in which all agents per default share the same performance evaluation rule, weighing past events strongly dramatically enhances the prevalence of cooperators. For co-evolutionary models, in which evaluation time horizons and strategies can co-evolve, I demonstrate that cooperation naturally associates with long-term evaluation of others while defection is typically paired with very short time horizons. Moreover, considering the continuous spectrum in between enhanced and discounted weights of past performance, cooperation is optimally supported when cooperators neither give enhanced weight to past nor more recent events, but simply average payoffs. Payoff averaging is also found to emerge as the dominant strategy for cooperators in co-evolutionary models, thus proposing a natural route to the evolution of cooperation in viscous populations

Preferential opponent selection in public goods games

This paper discusses preferential opponent selection in public goods games. It is shown that a preference to play with successful opponents strongly enhances the prevalence of cooperation. The finding is robust on spatial grids and heterogeneous networks. Importantly, I also demonstrate that positive opponent selection biases can evolve and become dominant in initially randomly mixed populations without selection bias

Optimizing spatially embedded networks for synchronization

In this paper we consider the problem of organizing networks of spatially embedded oscillators to maximize the propensity for synchronization for limited availability of wire, needed to realize the physical connections between the oscillators. We consider two extensions of previous work (Brede, 2010b): (i) oscillators that can flexibly arrange in space during the optimization process and (ii) a generalization to weighted networks. In the first case, we discuss the emergence of spatially and relationally modular network organizations, while in the second case the emphasis of our analysis is on link heterogeneity and the particular organization of strong and weak links that facilitates synchronization in space

A k-deformed Model of Growing Complex Networks with Fitness

The Barab\'asi-Bianconi (BB) fitness model can be solved by a mapping between the original network growth model to an idealized bosonic gas. The well-known transition to Bose-Einstein condensation in the latter then corresponds to the emergence of "super-hubs" in the network model. Motivated by the preservation of the scale-free property, thermodynamic stability and self-duality, we generalize the original extensive mapping of the BB fitness model by using the nonextensive Kaniadakis k-distribution. Through numerical simulation and mean-field calculations we show that deviations from extensivity do not compromise qualitative features of the phase transition. Analysis of the critical temperature yields a monotonically decreasing dependence on the nonextensive parameter k

Quantitative modelling of the human–Earth System a new kind of science?

The five grand challenges set out for Earth System Science by the International Council for Science in 2010 require a true fusion of social science, economics and natural science—a fusion that has not yet been achieved. In this paper we propose that constructing quantitative models of the dynamics of the human–Earth system can serve as a catalyst for this fusion. We confront well-known objections to modelling societal dynamics by drawing lessons from the development of natural science over the last four centuries and applying them to social and economic science. First, we pose three questions that require real integration of the three fields of science. They concern the coupling of physical planetary boundaries via social processes; the extension of the concept of planetary boundaries to the human–Earth System; and the possibly self-defeating nature of the United Nation’s Millennium Development Goals. Second, we ask whether there are regularities or ‘attractors’ in the human–Earth System analogous to those that prompted the search for laws of nature. We nominate some candidates and discuss why we should observe them given that human actors with foresight and intentionality play a fundamental role in the human–Earth System. We conclude that, at sufficiently large time and space scales, social processes are predictable in some sense. Third, we canvass some essential mathematical techniques that this research fusion must incorporate, and we ask what kind of data would be needed to validate or falsify our models. Finally, we briefly review the state of the art in quantitative modelling of the human–Earth System today and highlight a gap between so-called integrated assessment models applied at regional and global scale, which could be filled by a new scale of model

Planar growth generates scale free networks

In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not cross. The resulting network has a power law degree distribution, high clustering and the small world property. We argue that these characteristics are a consequence of the two defining features of the network formation procedure; growth and planarity conservation. We demonstrate that the model can be understood as a variant of random Apollonian growth and further propose a one parameter family of models with the Random Apollonian Network and the Deterministic Apollonian Network as extreme cases and our model as a midpoint between them. We then relax the planarity constraint by allowing edge crossings with some probability and find a smooth crossover from power law to exponential degree distributions when this probability is increased.Comment: 27 pages, 9 figure

Effects of Time Horizons on Influence Maximization in the Voter Dynamics

In this paper we analyze influence maximization in the voter model with an active strategic and a passive influencing party in non-stationary settings. We thus explore the dependence of optimal influence allocation on the time horizons of the strategic influencer. We find that on undirected heterogeneous networks, for short time horizons, influence is maximized when targeting low-degree nodes, while for long time horizons influence maximization is achieved when controlling hub nodes. Furthermore, we show that for short and intermediate time scales influence maximization can exploit knowledge of (transient) opinion configurations. More in detail, we find two rules. First, nodes with states differing from the strategic influencer's goal should be targeted. Second, if only few nodes are initially aligned with the strategic influencer, nodes subject to opposing influence should be avoided, but when many nodes are aligned, an optimal influencer should shadow opposing influence.Comment: 22 page