Sociophysics

The dynamics of a one dimensional Ising spin system is investigated using three families of local update rules, the Galam majority rules, Glauber inflow influences and Sznadj outflow drives. Given an initial density p of up spins the probability to reach a final state with all spins up is calculated exactly for each choice. The various formulas are compared to a series of previous calculations obtained analytically using the Kirkwood approximation. They turn out to be identical. The apparent discrepancy with the Galam unifying frame is addressed. The difference in the results seems to stem directly from the implementation of the local update rule used to perform the associated numerical simulations. The findings lead to view the non stepwise exit probability as an artifact of the one dimensional finite size system with fixed spins. The suitability and the significance to perform numerical simulations to model social behavior without solid constraints is discussed and the question of...

At the dawn of the third millennium, humanity is increasingly aware that its traditional ethnocentric ethic is inadequate for the task of global sustainability. It is by now apparent that the contradictory requirements of physical nature, modern culture and human nurture, demand an evolving and dynamic homeostasis among all three existential realms. Under the circumstances, traditional morality may seem too restricted in time and place to suffice in the interdependent and interacting world of the present and future. Yet, it is the fundamental axiom of this paper that updating, enlarging and readapting the classic cannon of ethics as a Modern Macro-Morality (M3) is the best way of resolving some of our planetary problems. In the Emerging Global Order (EGO) of the new millennium, renewed ethics will have to be applied in an ecumenical scale in order to harmonize both the potentiality and responsibility of humanity towards itself and its environment. Building a holistic ethic can only be done by transcending local particularities and emphasizing global similarities, found in all great philosophies, ideologies and religions. A distillation of the essence of these ideas indicates the shared deontology of our species. These human universals are firmly rooted in the implicate order of things from which they draw their common heritage and to which they eventually return. The primordial origin of this particular study is classic natural law as the eternal foundation of a renewed cosmopolitan ethic. This latest reinterpretation of ancient wisdom takes into account the recent advances of chaos and quantum theories as they have been worked out by the new paradigm of Sociophysics. Upon this natural infrastructure, the study here adds the social superstructure to form a physics-ethics-politics (PEP) hypothesis, explicating the relationship among these three crucial variables. The resulting thesis elaborated here is that a New Cosmic Morality would consist of minimal principles of mutual consideration, applied to a maximal extent consistent with political moderation and natural evolution. The study undertakes to define the concept, develop the process and decide the practice of ethics by posing nine critical questions and proposing their debatable answers. On the basis of this PEP discussion, a reformed theory of ethics could be elaborated eventually to serve the EGO of the new century.

We present a model of a prison with two types of inmates. One (recidivists) is a better organized and has more influence on the formation of opinions, whereas the second one is more susceptible to the influence of internal and external pressure. We study, via computer simulations, the interplay between well-organized minority and the rest and how the final decision, like e.g. starting a riot, depends on such factors as: fraction of recidivists, their initial support of the riot and possibility of contacts among cells. We find that, as expected, the riot is more likely to start if there is more recidivists favoring it at the beginning. The influence of external factors (media) turned out to have a larger impact on the second group of prisoners. Contrary to a common practice, we show that in order to prevent riots it might be better not to block the inter-cell contacts.

We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data.

An attempt to order the principal parameters of scientific theory into a holistic picture. To this end was constructed a System Unification Model to serve as a formal frame classifying the salient structures and functions of empirical existence. This SUM was used in the Sociophysics monograph published by Nova Science in 2000.

This study describes and explains the triangular relationships among the functional concepts of dialectics, politics and cybernetics on the basis of the new Theory of Sociophysics.      According to this theory natural and cultural systems share common roots and significant similarities, therefore they are best understood by a Single Unified Model.

The impact of wine experts, wine critics continue influencing the wine market, bloggers of wine lovers suggest personal judgments and give comments on wines they consume. Our work focuses on the impact of wine expert judgments versus the word-to-mouth effect on the dynamics of wine purchasing behavior.

We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolize the connections, while most other nodes are sparsely connected. Interestingly, this results in the protection of the less massive clusters from annihilation, to which the hubs are doomed.

Illusory projection along the arrow of time?
Visual indication of the cognitive challenge of a "hole" in time
Paradox of linear versus circular time: strange loops
Clues to distinguishing "degrees of intensity"
Temporal inversion and higher derivatives of time
Psychosocial implication of jerk, jolt, jounce and snap?
From sociophysics to learning to jounce?
Varieties of recognition in practice of an elusive missing dimension
Clues to experience of higher derivatives of time
Higher degrees of comprehension and their "compactification"?

Although all organisms affect their environment in order to survive, humanity has gone beyond all other species in transforming its natural habitat into an artificial one. This development is a result of the human capacity to envision ideal worlds and then try to realize them. External constraints, of course, do not always allow humankind's internal ideals to be implemented and thus sets the stage for the tragedy of the human condition. . In this article, we shall present a systematic method which could help us understand these problems and undertake their solutions. This method is based on the theory of sociophysics which developed its form and content through a Systems Unification Model (SUM). Sociophysics is an interdisciplinary theory which tries to establish linkages among the natural, social, and human sciences through unifying metaphors. On the basis of this unity, it will be possible to distinguish the different maleability potentials of the various domains of reality and thus optimize our impact upon them. Thus, sociophysics could show the way towards not only the most efficient and effective policies, but also the most ethical and aesthetic ones.

We study a spatial Prisoner’s dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner’s Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor’s strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategies; therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.

Illusory projection along the arrow of time?
Visual indication of the cognitive challenge of a "hole" in time
Paradox of linear versus circular time: strange loops
Clues to distinguishing "degrees of intensity"
Temporal inversion and higher derivatives of time
Psychosocial implication of jerk, jolt, jounce and snap?
From sociophysics to learning to jounce?
Varieties of recognition in practice of an elusive missing dimension
Clues to experience of higher derivatives of time
Higher degrees of comprehension and their "compactification"?

The study of formations and dynamics of opinions leading to the so called opinion consensus is one of the most important areas in mathematical modeling of social sciences. Following the Boltzmann type control recently introduced in [1], we consider a group of opinion leaders which modify their strategy accordingly to an objective functional with the aim to achieve opinion consensus. The main feature of the Boltzmann type control is that, thanks to an instantaneous binary control formulation, it permits to embed the minimization of the cost functional into the microscopic leaders interactions of the corresponding Boltzmann equation. The related Fokker-Planck asymptotic limits are also derived which allow to give explicit expressions of stationary solutions. The results demonstrate the validity of the Boltzmann type control approach and the capability of the leaders control to strategically lead the followers opinion.

Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with experimental neuroscience data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with ...

This paper studies the long-range dependence and multifractal content of U.S. political time-series to gather a deeper understanding of sociophysic phenomena. Specifically, multifractal detrended fluctuation analysis (MF-DFA) is applied upon data in the context of (i) president approval (polls), (ii) president online attention (Google Trends) and (iii) election-win probabilities (prediction markets). All analyzed series are characterized by anti-persistence, which may be interpreted as a nervous and overreacting behavior. We further detect significant multifractality with true non-linear correlation remaining after correcting for spurious sources. Importance from understanding the multifractal behavior arises from the fact that all three data types are used in practice for the prediction of election outcomes. We further argue that variation in local persistence (as implied by multifractality) can be both beneficial and destructive in different real-world scenarios. We draw parallels to simple examples like the timing of political campaigns or trading on prediction markets. On the methodological side, the article implements recent improvements of MF-DFA such as focus-based regression and overlapping segments.

Motivated by the seemingly chaotic state of affairs of contemporary world political actions, I describe a possible psychological masses domination strategy called " contradictory stimulation ". Assuming that there is the possibility of a genuine intention on the part of some families and powerful organizations in guiding humanity in the way of their interests, I point through mathematical and computational models that contradictory stimulation can be effective in inducing a subservient mentality in the political citizens. Recognize the existence of artful stratagems of manipulation and " brainwashing " sharpens our critical sense and changes our world view. It is the first step in a reaction that try to ensure individual freedoms, if they are desirable.

This paper was prepared for the Third Triple Helix International Conference held in Rio de Janeiro, April 2000.The study makes attempts to recapture the fundamental requirements of formal social science models, relying on the general Systems Unification Model of Sociophysics, whose interactive Triadic Interface Paradigm juxtaposes nature-culture-nurture as the three central aspects of human reality.

Terrorists usually choose to attack soft targets, with low self-protection abilities and resistance strengths, such as schools, campus, public squares, railway stations, etc. Under great panic, civilians attacked tend to escape aimlessly and disorderly. Hence, colliding, pushing, and trampling will take place and lead to indirect deaths and injuries. If some heroes with the spirit of altruism, coming from civilians, stand up and fight terrorists bravely, the injuries and deaths will be greatly reduced. Agentbased modeling is built to explore the role of heroes during terrorist attacks. The particle system of three categories of agents, civilians, terrorists & heroes, is built to simulate the Peshawar School Case in 2014. Multiple action rules and mechanisms are introduced, such as swarm intelligence, information communication, self-organized behaviors, and heroic behaviors. We run each simulation repeatedly for 100 times to obtain averaged (robust) outcomes. The optimal combination of parameters, which best matches real outcomes, will be solved accordingly. It indicates that: (a) the self-organizing of crowd behaviors greatly improves the survival rate of civilians. Hence, well-planned trainings of counterterrorists emergence responses can enhance capabilities of civilians; (b) people should learn from birds' swarm behavior in crowd evacuations. As a swarm intelligence pathway, small groups and information sharing during crowd escape simulations can greatly improve survival rates; and (c) the society should encourage more people to be altruistic heroes who are acting prosocially. Besides, it suggests that more heroes bring safer overall outcomes for civilians and even for heroes themselves.

This paper correlates the content of the social system to its context of the natural environment, Ecopolitics combines the concepts of ecology and polity, the former in its holistic and the latter in its cybernetic sense. This distinction emphasising the direct interrelations between the cultural and natural aspects of public affairs.

Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with those that characterize moral judgment patterns of conservatives and liberals.

In this paper, we study the effects of introducing contrarians in a model of Opinion Dynamics where the agents have internal continuous opinions, but exchange information only about a binary choice that is a function of their continuous opinion, the CODA model. We observe that the hung election scenario that arises when contrarians are introduced in discrete opinion models still happens. However, it is weaker and it should not be expected in every election. Finally, we also show that the introduction of contrarians make the tendency towards extremism of the original model weaker, indicating that the existence of agents that prefer to disagree might be an important aspect and help society to diminish extremist opinions.

Understanding the emergence of extreme opinions and in what kind of environment they might become less extreme is a central theme in our modern globalized society. A model combining continuous opinions and observed discrete actions (CODA) capable of addressing the important issue of measuring how extreme opinions might be has been recently proposed. In this paper I show extreme opinions to arise in a ubiquitous manner in the CODA model for a multitude of social network structures. Depending on network details reducing extremism seems to be possible. However, a large number of agents with extreme opinions is always observed. A significant decrease in the number of extremists can be observed by allowing agents to change their positions in the network.

A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction between neighbors, and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.

We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolise the connections, while most other nodes are sparsely connected. Interestingly, this results in the protection of the less massive clusters from annihilation, to which the hubs are doomed.

For an organisation with a Pareto-like distribution of the relevant resources we determine the social free energy and related social quantities using thermodynamical formalism. Macroscopic dynamics of the organisation is linked with the changes in the attributed thermodynamical quantities through changes in resource distribution function. It is argued that quantities of thermodynamical origin form the optimised set of organisation&#39;s state indicators, which is reliable expression of micro-dynamics.

This Article attempts to construct the proper ideals for the new Millennium, so that humanity could optimize its fundamental  values by improving their synergy with natural laws. This focus is based on the Sociophysics paradigm converging and integrating the basic aspects of nature and culture, thus resolving the contradictions of industrial competition and commercial globalization.

An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and longterm cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are intensively studied, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a high-dimensional analysis of the scientific beliefs of thousands of Europeans. We find that interopinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space. When empirical data are used as inputs in models, ultrametricity has strong and counterintuitive effects. On short timescales, it facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long timescales, it suppresses cultural convergence by restricting it within disjoint groups. Moreover, ultrametricity implies that these results are surprisingly robust to modifications of the dynamical rules considered. Thus the empirical distribution of individuals in cultural space appears to systematically optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence in a diverse range of online and offline settings.

The recent 2013 Italian elections are over and the situation that President Napolitano will have to settle soon for the formation of the new government is not the simplest one. After twenty years of bipolarism (more or less effective), where we were accustomed to a tight battle between two great political coalitions, the center-right and center-left, now, in the new Parliament, we have four political formations.

There are many studies in the marketing and diffusion literature of the conditions in which social contagion affects adoption processes. Yet most of these studies assume that social interactions do not change over time, even though actors in social networks exhibit different likelihoods of being influenced across the diffusion period. Rooted in physics and epidemiol- ogy theories, this study proposes a Susceptible Infectious Susceptible (SIS) model to assess the role of social contagion in adoption processes, which takes changes in social dynamics over time into account. To study the adoption over a span of ten years, the authors used detailed data sets from a community of consumers and determined the impor- tance of social contagion, as well as how the interplay of social and non-social influences from outside the community drives adoption processes. Although social contagion matters for diffusion, it is less relevant in shaping adoption when the study also includes social dynamics among members of the community. This finding is relevant for managers and entrepreneurs who trust in word-of-mouth marketing campaigns whose effect may be over- estimated if marketers fail to acknowledge variations in social interactions.

In this task we study the problem of coalition-fragmentation of 5 countries in the framework of Galam's Coliation Dynamics. Firstly, we introduce the Galam formalism and its application to the 2 and 3-country problem.  Then, we analyze a specific configuration in a 5-country network. An acceptance-rejection algorithm is proposed to simulate the coalition dynamics and results are obtained. Finally, a dissertation about possible extensions and generalizations of Galam model is offered.

Tusquets, Barcelona 236 pp. 18 € ¿Cómo pueden los físicos ser útiles para estudiar el comportamiento de los humanos si este comportamiento está guiado por intenciones mientras que los físicos se las tienen que ver con las conductas de átomos, moléculas y otras entidades descerebradas? Ésta es, suponemos, la pregunta que cualquiera se haría. Parte de la respuesta está en que una porción sustancial de cuanto ocurre en sociedad es «resultado de la acción humana, no del designio humano», como diría el pensador escocés del siglo XVIII Adam Ferguson. Los senderos que se abren en un bosque, la evolución de un idioma, la aparición del dinero como medio de cambio, la contaminación atmosférica en una ciudad o el mismo curso global de la historia son el resultado de lo que han hecho y están haciendo muchos cientos de miles de seres humanos, en diferentes épocas y sin obedecer a ningún plan de coordinación central; es decir, cuanto sucede en estos ámbitos, sucede al margen de su voluntad y sus propósitos, aunque, por otro lado, no cabe duda de que son sus actos, guiados por otros motivos conscientes, los que hacen posible la aparición y decurso de estos fenómenos sociales. Estos son los subproductos colectivos, para cuyo estudio no necesitamos reparar en las intenciones de cada sujeto particular, pues estas intenciones apuntan en otra dirección y no son las que explican la emergencia y evolución de tales subproductos. Como ya dijera Karl Popper, inspirado en ideas de Carl Menger y Friedrich Hayek: «Debemos admitir, sí, que la estructura de nuestro medio social es obra del hombre en cierto sentido, que sus tradiciones e instituciones no son ni la obra de Dios ni de la naturaleza, sino el resultado de las acciones y decisiones humanas, pudiendo ser modificadas, asimismo, por éstas; pero insistimos en que esto no significa que hayan sido diseñadas conscientemente y que sean explicables en función de necesidades, esperanzas o móviles. Muy por el contrario, aun aquellas que surgen como resultado de acciones humanas conscientes e intencionales son, por regla general, los subproductos indirectos, involuntarios, y frecuentemente no deseados, de dichas acciones »[1] . Según el mismo Popper, el campo de estudio propio de la sociología son estos subproductos colectivos, lo que, de ser cierto, significaría que la sociología se puede relevar del análisis de algunas de las complejidades psicológicas del ser humano (si bien no de todas ellas), y que las interacciones humanas que dan pie a la aparición de estos subproductos colectivos pueden ser «aproximadas» mediante los modelos de Página 1 de 8

In the context of an extension of Axelrod&apos;s model for social in uence, we study the interplay and competition between the cultural drift, represented as random perturba-tions, and mass media, introduced by means of an external homogeneous eld. Unlike previous studies [J. C. Gonzalez-Avella et al., Phys. Rev. E 72, 065102(R) (2005)], the mass media coupling proposed here is capable of aecting the cultural traits of any in-dividual in the society, including those who do not share any features with the external message. A noise-driven transition is found: for large noise rates, both the ordered (cul-turally polarized) phase and the disordered (culturally fragmented) phase are observed, while, for lower noise rates, the ordered phase prevails. In the former case, the external eld is found to induce cultural ordering, a behavior opposite to that reported in pre-vious studies using a dierent prescription for the mass media interaction. We compare the predictions of this model to stat...

Many socioeconomic studies have been carried out to explain the phenomenon of gentrification. Although results of these works shed light on the process around this phenomenon, a perspective which focuses on the relationship between city form and gentrification is still missing. With this paper we try to address this gap by studying and comparing, through classic methods of mathematical statistics, morphological features of five London gentrified neighbourhoods. Outcomes confirm that areas which have undergone gentrification display similar and recognizable morphological patterns in terms of urban type and geographical location of main and local roads as well as businesses. These initial results confirm findings from previous research in urban sociology, and highlight the role of urban form in contributing to shape dynamics of non-spatial nature in cities.

A simple model describing the dynamics of opinion forming in a two-party society is presented. Using a Monte Carlo simulation, we show what is the role played by the mobility of the electorate and the size of the groups within which opinions are exchanged. Each individual is characterized by its opinion and its susceptibility to the influence of others. We show what is the effect for a party to have a small percentage of supporters who will never change their mind. We determine when a party having at the beginning a smaller number of supporters, could nevertheless win democratic elections. The influence of an external random field (media) is also discussed.

We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolise the connections, while most other nodes are sparsely connected. Interestingly, this results in the protection of the less massive clusters from annihilation, to which the hubs are doomed.

Some mighty and prosperous empires of the past collapsed. Explanations why successful
civilizations collapsed disagree even about what collapse means. In fields like Physics,
Engineering and Biomathematics, collapse is a response of a system in unstable equilibrium
to a perturbation. This work applies the mathematical formulation of classical
stability theory to study socio-economic collapse. The model illustrates that increasing
complexity invariably explains collapse. This finding agrees with other scholars, however
the results dispute the need of associated factors like diminishing marginal returns,
excessive complexity growth rate or the relationship between frequency of perturbation and
their magnitude (references provided). Moreover, in previous works the term complexity
envelops a variety of elements. The approach of this work numerically defines complexity.
Such a definition allows unambiguously comparing the complexity of various societies.
The paper brings an incremental contribution to archaeological and historical debates,
by using classical stability theory for modeling complex socio-political systems.
Applying classical stability models in society allows a rigorous interpretation of concepts
used in archaeology as sustainability (equilibrium) or resiliency (stability).
The investigation shows that the transition of a stable equilibrium to an unstable
one may take centuries; nevertheless, the failure is abrupt. The article discusses why
associating various past societal collapses with a wide range of other causes does not
contradict the model.

An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and long-term cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are well understood, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a highdimensional analysis of the scientific beliefs of thousands of Europeans. We find that inter-opinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space, a result unaccessible to one-dimensional analyses and in striking contrast with random assumptions. When empirical data are used as inputs in models, we find that ultrametricity has strong and counterintuitive effects, especially in the extreme case of long-range online-like interactions bypassing social ties. On short time-scales, it strongly facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long time-scales, it severely suppresses cultural convergence by restricting it within disjoint groups. We therefore find that, remarkably, the empirical distribution of individuals in cultural space appears to optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence. This also shows that long-range interactions may simultaneously enhance coordination and sustain diversity.

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.

The concept of power is a fundamental notion in the human vocabulary. Yet, as old and venerable as it is, common sense and expert opinion alike have great difficulty in coming to grips with its nature or essence. It seems that power is a many splendored thing, depending on the point of view of the beholder.This problem of conceptualization is particularly acute between the natural and social sciences. Although the former has a clear position and rigorous definition of the term, the latter is still fuzzy on the concept and moot in its exact meaning; a situation that creates great difficulties and constant misunderstandings, especially in interdisciplinary discourse.The present study attempts to resolve these semantic issues, thus increasing human comprehension of this phenomenon and improving our ability to deal with it. That is done by extending General Systems Theory into a Sociophysics paradigm. This most recent exploration into scientific integration begins with a metaphoric transposition and ends with a symmetric composition leading towards that distant Grand Unified Theory at the end of the enlightenment tunnel. As a small step towards a general theory of power, this study focuses on power politics as a quintessential example of a natural-cultural metaphor. Consequently the central thesis here is that a rigorous definition of power can be similarly, easily and usefully applied to all three realms of reality: intrapersonal, interpersonal and extrapersonal. As a result of a more exact denotation and more widely shared connotation of the term, one should be in a better position to understand its manifold manifestations and control its multiple applications.This paper will therefore proceed deductively: first by inscribing the nominal definition of general concepts, then describing their actual manifestation in reality, and finally concluding by prescribing some ideal solution to their problems.