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

Replication strategies and the evolution of cooperation by exploitation

Introducing the concept of replication strategies this paper studies the evolution of cooperation in populations of agents whose offspring follow a social strategy that is determined by a parent's replication strategy. Importantly, social and replication strategies may differ, thus allowing parents to construct their own social niche, defined by the behaviour of their offspring. We analyse the co-evolution of social and replication strategies in well-mixed and spatial populations. In well-mixed populations, cooperation-supporting equilibria can only exist if the transmission processes of social strategies and replication strategies are completely separate. In space, cooperation can evolve without complete separation of the timescales at which both strategy traits are propagated. Cooperation then evolves through the presence of offspring exploiting defectors whose presence and spatial arrangement can shield clusters of pure cooperators

The coevolution of costly heterogeneities and cooperation in the prisoner's dilemma game

This paper discusses the co-evolution of social strategies and an efficiency trait in spatial evolutionary games. The continuous efficiency trait determines how well a player can convert gains from a prisoner's dilemma game into evolutionary fitness. It is assumed to come at a cost proportional to its magnitude and this cost is deducted from payoff. We demonstrate that cost ranges exist such that the regime in which cooperation can persist is strongly extended by the co-evolution of efficiencies and strategies. We find that cooperation typically associates with large efficiencies while defection tends to pair with lower efficiencies. The simulations highlight that social dilemma situations in structured populations can be resolved in a natural way: the nature of the dilemma itself leads to differential pressures for efficiency improvement in cooperator and defector populations. Cooperators benefit by larger improvements which allow them to survive even in the face of inferior performance in the social dilemma. Importantly, the mechanism is possible with and without the presence of noise in the evolutionary replication process

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