Axelrod Model Research Articles

Continuous Vector-Based Entropy Measurement on the Organizational Culture Evaluation

It is believed that organizational culture is one of the primary strategies that drive employee productivity and competitiveness. The abstract of organizational culture is a complex and dynamic phenomenon and challenge in the field of research till the present. The efficacy of human interaction with an organization is closely related to the propagation of organizational culture. In the meantime, cultural entropy is a metric for assessing the process of cultural dissemination in organizations, where a reduced entropy value is preferable. This study aims to modify the entropy culture algorithms that accommodate discrete and continuous vectors. We applied Shanon’s entropy as the fundamental formulation and the Axelrod model as the peer interaction analysis. The proposed measurement of cultural entropy considers not only the desired values but also evaluates the gap with the espoused value of the organization. The modified cultural entropy algorithm can measure the entropy value for discrete and continuous vectors. Measuring cultural entropy using continuous data results in an approach that can better display value heterogeneity within organizations.

Weighted Axelrod model: Different but similar

The Axelrod model is a cellular automaton which can be used to describe the emergence and development of cultural domains, where culture is represented by a fixed number of cultural features taking a discrete set of possible values (traits). The Axelrod model is based on two sociological phenomena: homophily (a tendency for individuals to form bonds with people similar to themselves) and social influence (the way how individuals change their behavior due to social pressure). However, the Axelrod model does not take into account the fact that cultural attributes may have different significance for a given individual. This is a limitation in the context of how the model reflects mechanisms driving the evolution of real societies. The study aims to modify the Axelrod model by giving individual features different weights that have a decisive impact on the possibility of aligning cultural traits between (interacting) individuals. The comparison of the results obtained for the classic Axelrod model and its modified version shows that introduced weights have a significant impact on the course of the system development, in particular, increasing the final fragmentation of the system and increasing the time needed to reach the final state.

Cultural heterogeneity constrains diffusion of innovations

Rogers' diffusion of innovations theory asserts that the cultural similarity among individuals plays a crucial role on the acceptance of an innovation in a community. However, most studies on the diffusion of innovations have relied on epidemic-like models where the individuals have no preference on whom they interact with. Here, we use an agent-based model to study the diffusion of innovations in a community of synthetic heterogeneous agents whose interaction preferences depend on their cultural similarity. The community heterogeneity and the agents' interaction preferences are described by Axelrod's model, whereas the diffusion of innovations is described by a variant of the Daley and Kendall model of rumour propagation. The interplay between the social dynamics and the spreading of the innovation is controlled by the parameter , which yields the probability that the agent engages in social interaction or attempts to spread the innovation. Our findings support Roger's empirical observations that cultural heterogeneity curbs the diffusion of innovations.

Emergence of Social Norms in Metanorms Game With High-Order Interaction Topology

In an autonomous system, rational agents aim to maximize their benefits. Rational agents gradually give up cooperation with others and only request services, which leads to the phenomenon of free-riding. This phenomenon generally exists in the real society and application system. Therefore, how to reduce the behavior, which is similar to free-riding, has become an important research topic. In addition, the traditional pairwise interaction network cannot truly reflect the interaction properties of cooperative events. Social norms provide an effective way to promote cooperation for autonomous systems. Axelrod's metanorm game model achieves the emergence of social norms by conducting punishment to connivance based on punishing defection. However, links in networks only allow for pairwise interactions. Therefore, we introduce hypergraphs, which are more suitable to reflect group interaction to model metanorm games. The establishment efforts of norms are examined on hypergraphs (uniform random hypergraph (URH), hyperdegree-heterogeneous random hypergraphs, and real-world hypergraphs). We show that the difference in group sizes affects norms emergence of agents and realize the establishment of social norms on URH. To a certain extent, the probability of being seen is positively correlated with agents' vengefulness and learning time and negatively correlated with boldness. However, the usage of the boldness and vengefulness learning (BV-learning) algorithm on HRHs cannot make norms emergence because leavers cannot participate in learning and the fixed learning step. Therefore, we propose the dynamic relevance BV-learning algorithm to overcome the aforementioned problems, so hub agents and leavers can jointly establish better social norms. We also verify the evolution process of agents' cooperation rate by BV-learning and the dynamic relevance BV-learning, respectively, which demonstrate that the establishment of social norms can indeed promote agents' cooperation. Finally, in order to illustrate the universality of the dynamic relevance BV-learning clearly, we study norms establishment on real-world hypergraphs by and compare it with BV-learning. It can be found that the dynamic relevance BV-learning can effectively establish social norms on real-world hypergraphs.

Dyadic Interaction Shapes Social Identity in the Axelrod Model Using Empirical Data

Dyadic Interaction Shapes Social Identity in the Axelrod Model Using Empirical Data

Spectral Analysis of Multiscale Cultural Traits on Twitter

Understanding and mapping the emergence and boundaries of cultural areas is a challenge for social sciences. In this paper, we present a method for analyzing the cultural composition of regions via Twitter hashtags. Cultures can be described as distinct combination of traits which we capture via principal component analysis (PCA). We investigate the top 8 PCA components of an area including France, Spain, and Portugal, in terms of the geographic distribution of their hashtag composition. We also discuss relationships between components and the insights those relationships can provide into the structure of a cultural space. Finally, we compare the spatial autocorrelation of PCA components in the Twitter data to similar components resulting from the Axelrod model. We conclude that properties of Twitter behavior can be framed in the discussion of cultural emergence and collective learning.

The consequences of hesitation: Axelrod model with intrinsic noise.

We study the influence of hesitating agents in the Axelrod model by introducing an intrinsic noise, which is proportional to the disagreement between the interacting agents, and thus coupled to the dynamics. Our results show that, unlike the effect of the cultural drift where the noise is just controlled by an external parameter, the intrinsic noise never allows the system to reach a frozen state in the thermodynamic limit. Moreover, we show that when the intrinsic noise affects the agents’ variables, the system’s behaviour is also different from the case when it affects the network of their interactions.

The Spread of Ideas in a Network-The Garbage-Can Model.

The main goal of our work is to show how ideas change in social networks. Our analysis is based on three concepts: (i) temporal networks, (ii) the Axelrod model of culture dissemination, (iii) the garbage can model of organizational choice. The use of the concept of temporal networks allows us to show the dynamics of ideas spreading processes in networks, thanks to the analysis of contacts between agents in networks. The Axelrod culture dissemination model allows us to use the importance of cooperative behavior for the dynamics of ideas disseminated in networks. In the third model decisions on solutions of problems are made as an outcome of sequences of pseudorandom numbers. The origin of this model is the Herbert Simon’s view on bounded rationality. In the Axelrod model, ideas are conveyed by strings of symbols. The outcome of the model should be the diversity of evolving ideas as dependent on the chain length, on the number of possible values of symbols and on the threshold value of Hamming distance which enables the combination.

Polarization inhibits the phase transition of Axelrod's model.

We study the effect of polarization in Axelrod's model of cultural dissemination. This is done through the introduction of a cultural feature that takes only two values, while the other features can present a larger number of possible traits. Our numerical results and mean-field approximations show that polarization reduces the characteristic phase transition of the original model to a finite-size effect, since at the thermodynamic limit only the ordered phase is present. Furthermore, for finite system sizes, the stationary state depends on the percolation threshold of the network where the model is implemented: a polarized phase is obtained for percolation thresholds below 1/2, and a fragmented multicultural one otherwise.

Homophily dynamics outweigh network topology in an extended Axelrod’s Cultural Dissemination Model

Personal social networks reveal potential sources of dyadic social influence. Social influence is picked up as a main principle of Axelrod’s model of cultural dissemination. Even though social influence is performed via social networks, the model is generally just run on a regular lattice instead of more complex network topologies. In this paper, we analyse a concurrent extension to Axelrod’s model for opinion-based groups, and explore the performance of changing the network topology.Our objective is to seed the Axelrod model with attitudinal survey data as an empirical data application. In the model, the culture is a set of features which in turn is defined by a set of traits. Respectively, in survey data, the attitudes are captured by items with a fixed set of response options. The direct correspondence of the structure of survey data to the model makes it an ideal candidate. Here, we simulate and analyse the extended Axelrod model to explore its dynamics and outcomes, with the standard Axelrod model results serving as a benchmark. As well as the lattice, which the Axelrod model is usually simulated on, we test other network topologies. The conducted simulations explore the parameter space for the uniformly distributed models, and draw parallels between the results, when applying it to an empirical, attitudinal data set.After assessing the level of impact of the network structures, we conclude that there is almost no influence of the underlying network structure on the macro level outcomes. The reason seems to be that the homophily structure among the individuals outweighs the impact of the network topology in the long run simulations. Under the premise, that the number of features is higher than the number of traits and that the system size is limited, the extended Axelrod model can be used to simulate attitudes from a survey — without specifying the underlying network.

Analytical approach to the Axelrod model based on similarity vectors.

Complex problems of social interaction are usually studied within the framework of agent-based models. Some of these problems, such as issue alignment and opinion polarization, are better suited in the framework of n-dimensional opinion space. Although this kind of complex problem may be explored by numerical simulations, these simulations can hinder our ability to obtain general results. In this work, we show how, under certain conditions, a classical multidimensional opinion model such as the Axelrod model can give rise to a closed set of master equations in terms of vector similarities between agents. The analytical results fully agree with the simulations on complete networks, accurately predict the similarity distribution of the whole system in sparse topologies, and provide a good approximation of the similarity of physical links that improves when the mean degree of the system increases.

Agreement threshold on Axelrod's model of cultural dissemination.

Shared opinions are an important feature in the formation of social groups. In this paper, we use the Axelrod model of cultural dissemination to represent opinion-based groups. In the Axelrod model, each agent has a set of features which each holds one of a set of nominally related traits. Survey data has a similar structure, where each participant answers each of a set of items with responses from a fixed list. We present an alternative method of displaying the Axelrod model by representing it as a bipartite graph, i.e., participants and their responses as separate nodes. This allows us to see which feature-trait combinations are selected in the final state. This visualisation is particularly useful when representing survey data as it illustrates the co-evolution of attitudes and opinion-based groups in Axelrod's model of cultural diffusion. We also present a modification to the Axelrod model. A standard finding of the Axelrod model with many features is for all agents to fully agree in one cluster. We introduce an agreement threshold and allow nodes to interact only with those neighbours who are within this threshold (i.e., those with similar opinions) rather than those with any opinion. This method reliably yields a large number of clusters for small agreement thresholds and, importantly, does not limit to single cluster when the number of features grows large. This potentially provides a method for modelling opinion-based groups where as opinions are added, the number of clusters increase.

Erdós-Rényi phase transition in the Axelrod model on complete graphs.

The Axelrod model has been widely studied since its proposal for social influence and cultural dissemination. In particular, the community of statistical physics focused on the presence of a phase transition as a function of its two main parameters, F and Q. In this work, we show that the Axelrod model undergoes a second-order phase transition in the limit of F→∞ on a complete graph. This transition is equivalent to the Erdős-Rényi phase transition in random networks when it is described in terms of the probability of interaction at the initial state, which depends on a scaling relation between F and Q. We also found that this probability plays a key role in sparse topologies by collapsing the transition curves for different values of the parameter F.

Symmetric group and the Axelrod model for dissemination of cultures

We review the Axelrod’s model for dissemination of cultures from an analytic point of view. We define ⟨s(t)⟩ to quantify possible culture configurations at time t in a society. Typical initial culture configurations of this model are characterised. Equation of motion in terms of ⟨s(t)⟩ is derived. We study the dynamic of this Axelrod system toward to its culture configurations equilibrium. Generically, we observe that this model undergoes three phases of development. We give a quantitative explanation about the latter. We characterize the culture configurations space at equilibrium point where 〈s(teq)〉=1. This space is called monoculture space. Understanding this space is equivalent to restrict to the space of culture configurations from one individual in the model. This individual cultural space is identified to the space VN⊗F up to isomorphisms. In this model, N and F are respectively the dimension and the number of attributes to define an individual state. VN is a N-dimensional vector space. Action of the permutation group SN on the space VN⊗F is considered. Under this action, the observable ⟨s(t)⟩ is an invariant of the Axelrod system. We explore this symmetry and classify the different inequivalent classes of culture configurations composing the monoculture space. To achieve this, we consider the case N ≥ F. We propose techniques from group representation theory to perform this classification. The inequivalent classes of culture configurations are indexed by the Dickau diagrams which are associated to the Bell number BF. A concrete example with F=4 and N ≥ 4 is considered for a full illustration of our analysis.

Adaptive rewiring of links in a network: Jammed states

We investigate stationary states produced within the limited version of the Axelrod model, where the dynamics is reduced to the rewiring, and the copying of states is switched off. The work function W is defined as the sum of Hamming distances between linked nodes. The rewiring occurs only if the work function does not increase. The state of a node is a chain of symbols, with the chain length F, and each symbol can admit one of q values. Initially, N actors are placed at randomly selected nodes-states, and L links are distributed between actors. Numerical calculations allow to identify ranges of parameters N,L,F,q where, for a given configuration of occupied states, W remains above its minimal value. These metastable configurations, termed here as jammed states, are shown to be abundant for L close to its limit values 1 and N(N−1)∕2−1, and rare or absent for intermediate connectivities. The simulations allow to evaluate the role of basins of attraction of the jammed states.

Dynamic evolution of economic networks under the influence of mergers and divestitures

Mergers and divestitures are two major economic activities. In this article, an evolutionary model combined with mergers and divestitures is proposed from the perspective of complex network science. More specifically, the Axelrod model is introduced to present the identity of entities on the economic network, the Cobb–Douglas production function is used to calculate the power of each entity, and the probabilities of mergers and divestitures are determined by the Fermi function considering key economic indicators during the evolution. We find that mergers and divestitures have neither good nor bad characteristics by themselves, and that the key to the success of these activities is the ability and the development status of entities in the economic network. Identity dimension, learning ability, initial network size, and density usually play important roles in the progress under the influence of mergers and divestitures. Power, degree, age, identity distance, maximal ingredient, network size, and the frequency of mergers and divestitures likewise can give rise to very different processes in different economic environments. The presented results may have a high reference value when economic sectors develop specific merger and divestiture policies, and we also outline directions for future research that seem important and promising along the same lines.

Microstructure and dielectric properties of BF\u2013PFN ceramics with negative dielectric loss

Multiferroics with negative value of dielectric constant are very promising materials because of their modern applicability. These materials can be used as materials for the construction of electromagnetic radiation shields. The subject of the research is multiferroic BiFeO3–PbFe1/2Nb1/2O3 (BF–PFN) ceramics. For all multiferroic materials the following studies are conducted: SEM, EDS and the temperature dependence of dielectric constant ε′(T). Above a certain temperature (different for different chemical compositions) the value of dielectric constant reaches negative values. Such the behavior of the dielectric constant may indicate that the polarization inside the material has a reverse direction to the external electric field. That is, the electric field inside the material counteracts the applied external electric field. The obtaining materials also show negative dielectric losses. The Axelrod model is used to explain the mechanism that causes negative dielectric loss.

Robustness of cultural communities in an open-ended Axelrod’s model

We consider an open-ended set of cultural features in the Axelrod model of cultural dissemination. By replacing the features in which a high degree of consensus is achieved by new ones, we address here an essential ingredient of societies: the evolution of topics as a result of social dynamics and debate. Our results show that, once cultural clusters have been formed, the introduction of new topics into the social debate has little effect on them, but it does have a significant influence on the cultural overlap. Along with the Monte Carlo simulations, we derive and numerically solve an equation for the stationary cultural overlap based on a mean-field approach which reproduces the qualitative behavior of the model.

Layered social influence promotes multiculturality in the Axelrod model

Despite the presence of increasing pressure towards globalisation, the coexistence of different cultures is a distinctive feature of human societies. However, how multiculturality can emerge in a population of individuals inclined to imitation, and how it remains stable under cultural drift, i.e. the spontaneous mutation of traits in the population, still needs to be understood. To solve such a problem, we propose here a microscopic model of culture dissemination which takes into account that, in real social systems, the interactions are organised in various layers corresponding to different interests or topics. We show that the addition of multiplexity in the modeling of our society generates qualitatively novel dynamical behavior, producing a new stable regime of cultural diversity. This finding suggests that the layered organisation of social influence typical of modern societies is the key ingredient to explain why and how multiculturality emerges and thrives in our world.

Effect of long-range interactions on the phase transition of Axelrod's model.

Axelrod's model with F=2 cultural features, where each feature can assume k states drawn from a Poisson distribution of parameter q, exhibits a continuous nonequilibrium phase transition in the square lattice. Here we use extensive Monte Carlo simulations and finite-size scaling to study the critical behavior of the order parameter ρ, which is the fraction of sites that belong to the largest domain of an absorbing configuration averaged over many runs. We find that it vanishes as ρ∼(q_{c}^{0}-q)^{β} with β≈0.25 at the critical point q_{c}^{0}≈3.10 and that the exponent that measures the width of the critical region is ν^{0}≈2.1. In addition, we find that introduction of long-range links by rewiring the nearest-neighbors links of the square lattice with probability p turns the transition discontinuous, with the critical point q_{c}^{p} increasing from 3.1 to 27.17, approximately, as p increases from 0 to 1. The sharpness of the threshold, as measured by the exponent ν^{p}≈1 for p>0, increases with the square root of the number of nodes of the resulting small-world network.