According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], ''the life of man [is] solitary, poor, nasty, brutish, and short,'' and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized control. The self-organization of cooperative behavior is particularly puzzling for social dilemmas related to sharing natural resources or creating common goods. Such situations are often described by the prisoner's dilemma. Here, we report the sudden outbreak of predominant cooperation in a noisy world dominated by selfishness and defection, when individuals imitate superior strategies and show success-driven migration. In our model, individuals are unrelated, and do not inherit behavioral traits. They defect or cooperate selfishly when the opportunity arises, and they do not know how often they will interact or have interacted with someone else. Moreover, our individuals have no reputation mechanism to form friendship networks, nor do they have the option of voluntary interaction or costly punishment. Therefore, the outbreak of prevailing cooperation, when directed motion is integrated in a game-theoretical model, is remarkable, particularly when random strategy mutations and random relocations challenge the formation and survival of cooperative clusters. Our results suggest that mobility is significant for the evolution of social order, and essential for its stabilization and maintenance.evolution ͉ pattern formation ͉ spatial games ͉ mobility ͉ migration

In this paper, a centrifugal force model is developed for pedestrian dynamics. The effects of both the headway and the relative velocity among pedestrians are taken into account, which can be expressed by a "centrifugal force" term in dynamic equation. The jamming probability due to the arching at exits for crowd flows is provided. A quantitative analysis of the crowd flowing out of a hall shows that the average leaving time T is a function of the exit width W in negative power. The related simulation indicates that the proposed model is able to reproduce the self-organization phenomena of lane formation for sparse flows.

A unified approach is proposed, which integrates game-theoretical models with models of directed motion. Specifically, strategic interactions in space and imitation of more successful neighboring strategies, as studied by spatial games, are combined with successdriven migration based on "test interactions" or wealth-related "neighborhood tagging." It turns out that such directed migration allows cooperators to evade defectors and (in constrast to purely diffusive motion) also to find other cooperators in order to form clusters ("islands of cooperation"). This can increase the cooperation to a great extent. Moreover, success-driven motion leads to interesting spatiotemporal pattern-formation phenomena, which are clearly different from those produced by previously studied spatial games. Despite the simplicity of the model, the forming patterns appear to realistically represent many stylized facts of social interactions, particularly phenomena such as social networking, urban aggregation, social segregation or turn-taking. Furthermore, migration games offer a game-theoretical explanation of social attraction and repulsion, based on payoff-related mobility, and they display a larger variety than conventional games, as their behavior is not invariant to shifting all payoffs by a constant amount. In summary, the combination of strategic interactions and imitation with models of directed motion has high potential for understanding empirical observations in the social, biological and economic sciences from a game-theoretical point of view. Finally, the breakdown of cooperation in the prisoner's dilemma at high values of temptation is explained by configurational analysis.

A recent study [D. Helbing, A. Johansson, and H. Z. Al-Abideen, Phys. Rev. E 75, 046109 (2007)] has revealed a "turbulent" state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling of people. However, turbulent crowd motion is not reproduced well by current many-particle models due to their insufficient representation of the local interactions in areas of extreme densities. In this contribution, we extend the repulsive force term of the social force model to reproduce crowd turbulence. We perform numerical simulations of pedestrians moving through a bottleneck area with this model. The transitions from laminar to stop-and-go and turbulent flows are observed. The empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments, are reproduced well; i.e., they are well compatible with an analysis of video data during the annual Muslim pilgrimage.