Opinion evolution in closed community

A simple Ising spin model which can describe a mechanism of making a decision in a closed community is proposed. It is shown via standard Monte Carlo simulations that very simple rules lead to rather complicated dynamics and to a power law in the decision time distribution. It is found that a closed community has to evolve either to a dictatorship or a stalemate state (inability to take any common decision). A common decision can be taken in a "democratic way" only by an open community.Comment: 13 pages, 7 figure

How effective is advertising in duopoly markets?

A simple Ising spin model which can describe the mechanism of advertising in a duopoly market is proposed. In contrast to other agent- based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among customers. It is shown via standard Monte Carlo simulations that very simple rules and inclusion of an external field - an advertising campaign - lead to phase transitions, ie. extreme and fast changes in market share.advertising, oligopoly, duopoly, Ising model, agent-based model

Evolution in a changing environment

We propose a simple model, based on Monte Carlo simulations, for studying the effects of changes in the environment on the adaptation and extinction of evolving species. We show that the geological data of climatic changes are well described by Levy-stable distributions. This leads, in our model, to a fairly good reproduction of the known data on species extinctions. We have also found that the dependence of the probability that a given number of species becomes extinct in one time step, on the number of extinct species shows a cross-over from an exponential to a power-like character.Levy-stable distribution; Monte Carlo simulation; Species extinction; Evolution;

Homogeneous symmetrical threshold model with nonconformity: independence vs. anticonformity

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and posses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, such as the majority-vote and the q-voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q-voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean-field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed, if the threshold r = 0.5, which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r > 0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.Comment: 12 pages, 4 figures, accepted to Complexit

Impact of memory on opinion dynamics

We investigate an agent-based model of opinion dynamics with two types of social response: conformity and independence. Conformity is introduced to the model analogously as in the Sznajd model or $q$-voter model, which means that only unanimous group exerts peer pressure on individuals. The novelty, in relation to previous versions of the $q$-voter model, is memory possessed by each agent and external noise $T$, which plays the role of social temperature. Each agent has its own memories of past experiences related to the social costs and benefits of being independent or conformist. If an agent was awarded in past more for being independent, it will have a greater tendency to be independent than conformist and vice versa. We will show that depending on the social temperature $T$ the system spontaneously organizes into one of two regimes. Below a certain critical social temperature $T_c$, all agents in the society acquire personal traits (so called person state). Some of them become permanent conformists and others start to behave forever independently. This means that initially homogeneous population becomes heterogeneous, and agents respond differently to social influence. For $T>T_c$, all agents with equal probabilities behave independently or conform to peer pressure (so called situation state). This regime change between person and situation state, which reminds the idea of an annealed vs. quenched disorder, affects also public opinion. Particularly interesting results are obtained for individualistic societies, in which public opinion is non-monotonic function of $T$, which means that there is an optimal social temperature for which an agreement in the society is the highest.Comment: 16 pages, 5 figures, (copyright) 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0