Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.Comment: 5 pages, 6 figure

X-ray and Radio Monitoring of GX 339-4 and Cyg X-1

Previous work by Motch et al. (1985) suggested that in the low/hard state of GX339-4, the soft X-ray power-law extrapolated backward in energy agrees with the IR flux level. Corbel and Fender (2002) later showed that the typical hard state radio power-law extrapolated forward in energy meets the backward extrapolated X-ray power-law at an IR spectral break, which was explicitly observed twice in GX339-4. This has been cited as further evidence that jet synchrotron radiation might make a significant contribution to the observed X-rays in the hard state. We explore this hypothesis with a series of simultaneous radio/X-ray hard state observations of GX339-4. We fit these spectra with a simple, but remarkably successful, doubly broken power-law model that indeed requires a spectral break in the IR. For most of these observations, the break position as a function of X-ray flux agrees with the jet model predictions. We then examine the radio flux/X-ray flux correlation in Cyg X-1 through the use of 15 GHz radio data, obtained with the Ryle radio telescope, and Rossi X-ray Timing Explorer data, from the All Sky Monitor and pointed observations. We find evidence of `parallel tracks' in the radio/X-ray correlation which are associated with `failed transitions' to, or the beginning of a transition to, the soft state. We also find that for Cyg X-1 the radio flux is more fundamentally correlated with the hard, rather than the soft, X-ray flux.Comment: To Appear in the Proceedings of "From X-ray Binaries to Quasars: Black Hole Accretion on All Mass Scales" (Amsterdam, July 2004). Eds. T Maccarone, R. Fender, L. H

A Tale of Two Selves

How did cooperation and communication evolve in human society? In a provocative Perspective, Sigmund and Nowak write about a recent meeting on this subject that drew comparisons between termites and humans, and genes and memes, and pointed out how irrational human behavior is a crucial (and often underestimated) component of economic exchange in human society

Super- and Coinfection: The Two Extremes

This paper investigates simplified models of multiple infection. Its first part deals with superinfection: the more virulent strain quickly outcompetes its rivals. The second part deals with coinfection: the rate of new infections produced by one strain is unaffected by the presence of other strains. The two cases differ in expectations for the resultant range of strains within the host population; they are similar in that both predict a considerable increase in virulence based on optimizing basic reproduction ratio of the pathogen do not work if several strains of pathogens compete within the host

Confinement, Turbulence and Diffraction Catastrophes

Many features of large N_c transition that occurs in the spectral density of Wilson loops as a function of loop area (observed recently in numerical simulations of Yang-Mills theory by Narayanan and Neuberger) can be captured by a simple Burgers equation used to model turbulence. Spectral shock waves that precede this asymptotic limit exhibit universal scaling with N_c, with indices that can be related to Berry indices for diffraction catastrophes.Comment: Presented at PANIC 200

Reward and Punishment in Minigames

Minigames capturing the essence of Public Goods experiments show that even in the absence of rationality assumptions, both punishment and reward will fail to bring about prosocial behavior. This holds in particular for the well-known Ultimatum Game, which emerges as a special case. But reputation can induce fairness and cooperation in populations adapting through learning or imitation. Indeed, the inclusion of reputation effects in the corresponding dynamical models leads to the evolution of economically productive behavior, with agents contributing to the public good and either punishing those who don't, or rewarding those who do. Reward and punishment correspond to two types of bifurcation with intriguing complementarity. The analysis suggests that reputation is essential for fostering social behavior among selfish agents, and that it is considerably more effective with punishment than with rewards

Fairness Versus Reason in the Ultimatum Game

In the Ultimatum Game, two players are offered a chance to win a certain sum of money. All they must do is divide it. The proposer suggests how to split the sum. The responder can accept or reject the deal. If the deal is rejected, neither player gets anything. The rational solution, suggested by game theory, is for the proposer to offer the smallest possible share and for the responder to accept it. If humans play the game, however, the most frequent outcome is a fair share. In this paper, we develop an evolutionary approach to the Ultimatum Game. We show that fairness will evolve if the proposer can obtain some information on what deals the responder has accepted in the past. Hence, the evolution of fairness, similar to the evolution of cooperation, is linked to reputation

Adaptive dynamics with interaction structure

Evolutionary dynamics depend critically on a population's interaction structure - the pattern of which individuals interact with which others, depending on the state of the population and the environment. Previous research has shown, for example, that cooperative behaviors disfavored in well-mixed populations can be favored when interactions occur only between spatial neighbors or group members. Combining the adaptive dynamics approach with recent advances in evolutionary game theory, we here introduce a general mathematical framework for analyzing the long-term evolution of continuous game strategies for a broad class of evolutionary models, encompassing many varieties of interaction structure. Our main result, the "canonical equation of adaptive dynamics with interaction structure", characterizes expected evolutionary trajectories resulting from any such model, thereby generalizing a central tool of adaptive dynamics theory. Interestingly, the effects of different interaction structures and update rules on evolutionary trajectories are fully captured by just two real numbers associated with each model, which are independent of the considered game. The first, a structure coefficient, quantifies the effects on selection pressures, and thus on the shapes of expected evolutionary trajectories. The second, an effective population size, quantifies the effects on selection responses, and thus on the expected rates of adaptation. Applying our results to two social dilemmas, we show how the range of evolutionarily stable cooperative behaviors systematically varies with a model's structure coefficient