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

Real Space Renormalization Group for Langevin Dynamics in Absence of Translational Invariance

A novel exact dynamical real space renormalization group for a Langevin equation derivable from a Euclidean Gaussian action is presented. It is demonstrated rigorously that an algebraic temporal law holds for the Green function on arbitrary structures of infinite extent. In the case of fractals it is shown on specific examples that two different fixed points are found at variance with periodic structures. Connection with growth dynamics of interfaces is also discussed.Comment: 22 pages, RevTex 3.0, 5 figures available upon request from [email protected], to be published in J.Stat.Phy

Collective pinning of a frozen vortex liquid in ultrathin superconducting YBa_2Cu_3O_7 films

The linear dynamic response of the two-dimensional (2D) vortex medium in ultrathin YBa_2Cu_3O_7 films was studied by measuring their ac sheet impedance Z over a broad range of frequencies \omega. With decreasing temperature the dissipative component of Z exhibits, at a temperature T*(\omega) well above the melting temperature of a 2D vortex crystal, a crossover from a thermally activated regime involving single vortices to a regime where the response has features consistent with a description in terms of a collectively pinned vortex manifold. This suggests the idea of a vortex liquid which, below T*(\omega), appears to be frozen at the time scales 1/\omega of the experiments.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Evolutionary prisoner's dilemma game on a square lattice

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing state when varying the value of temptation to defect. In the limits $c \to 0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.Comment: 6 pages including 6 figure

Statistical mechanics of complex networks

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic