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

Evolutionary prisoner's dilemma games with optional participation

Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This results in a rock-scissors-paper type cyclic dominance of the three strategies. The players are located either on square lattices or random regular graphs with the same connectivity. Occasionally, every player reassesses its strategy by sampling the payoffs in its neighborhood. The loner strategy efficiently prevents successful spreading of selfish, defective behavior and avoids deadlocks in states of mutual defection. On square lattices, Monte Carlo simulations reveal self-organizing patterns driven by the cyclic dominance, whereas on random regular graphs different types of oscillatory behavior are observed: the temptation to defect determines whether damped, periodic or increasing oscillations occur. These results are compared to predictions by pair approximation. Although pair approximation is incapable of distinguishing the two scenarios because of the equal connectivity, the average frequencies as well as the oscillations on random regular graphs are well reproduced.Comment: 6 pages, 7 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

Evolutionary Dynamics of Biological Games

Darwinian dynamics based on mutation and selection from the core of mathematical models for adaptation and coevolution of biological populations. The evolutionary outcome is often not a fitness-maximizing equilibrium but can include oscillations and chaos. For studying frequency-dependent selection, game-theoretic arguments are more appropriate than optimization algorithms. Replicator and adaptive dynamics describe short-and long-term evolution in phenotype space and have found applications ranging from animal behavior and ecology to speciation, macroevolution, and human language. Evolutionary game theory is an essential component of a mathematical and computational approach to biology

Social games in a social network

We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community

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