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    Evolutionary minority games with memory

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    We propose a simple dynamic adjustment mechanism, equivalent to the standard replicator dynamics in discrete time, to study the time evolution of a population of players facing a binary choice game, and apply this mechanism to minority games in order to investigate the effects of memory on the stability of the unique Nash equilibrium. Two different kinds of memory are considered, one where the players take into account the current and the previous payoffs in order to decide the strategy chosen in the next period, and the other one where the players consider the whole series of payoffs observed in the past through a discounted sum with exponentially fading weights. Both the memory representations proposed lead to an analytically tractable two-dimensional dynamical system, so that analytical results can be given for the stability of the Nash equilibrium. However, a global analysis of the models - performed by numerical methods and guided by the analytical results - shows that some complexities arise for intermediate values of the memory parameter, even if the stabilization effect of uniform memory is stated in both cases

    Minority influence in opinion spreading

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    Social influence has been an object of interest of social psychology for a long time. More recently, sociophysics and Galam's model provide an explanation of rumors spreading in a population explaining some interesting social phenomena as diffusion of false information. Although Galam's model and its recent formalizations are suitable to describe some social behavior, they take into account populations with homogeneous agents. Some recent contributions consider agents who do not change opinion and in some cases are able to persuade the others. Starting from social psychology studies about the role of specific seat occupation we provide a heterogeneous model in which those holding minority opinions can strategically choose specific social gatherings to exert their influence. We simulate the opinion dynamics comparing situations in which there is the minority to others with homogeneous agents. Our results show how the opinion dynamics is affected by the presence of such a minority

    Evolutionary dynamics in club goods binary games

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    A dynamic adjustment mechanism, based on replicator dynamics in discrete time, is used to study the time evolution of a population of players facing a binary choice game with social influence, characterized by payoff curves that intersect at two interior points, also denoted as thresholds. So, besides the boundary equilibria where all players make the same choice, there are two further steady states where agents playing different strategies coexist and get identical payoffs. Such binary game can be interpreted as a club good game, in which players have to choose either joining or not the club in the presence of cost sharing, so that they can enjoy a good or a service provided that a "participation" threshold is reached. At the same time congestion occurs beyond a second higher threshold. These binary choice models, can be used (and indeed have been used in the literature) to represent several social and economic decisions, such as technology adoption, joining a commercial club, R&D investments, production delocalization, programs for environmental protection. Existence and stability of equilibrium points are studied, as well as the creation of more complex attractors (periodic or chaotic) related with overshooting effects. The study of some local and global dynamic properties of the evolutionary model proposed reveals that the presence of the "participation" threshold causes the creation of complex topological structures of the basins of coexisting attracting sets, so that a strong path dependence is observed. The dynamic effects of memory, both in the form of convex combination of a finite number of previous observation (moving average) and in the form of memory with increasing length and exponentially fading weights are investigated as well

    Opinion dynamics on networks

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    Sociophysics has devoted a lot of attention to social influence and opinion dynamics. Among the others, the pioneering works by Galam, where agents randomly gather in groups of different size until consensus is reached, have been used to analyze the spreading of rumors. Galam's model however, considers only special kinds of social spaces. In this chapter we survey some of the most recent contributions on opinion dynamics, illustrate Galam's model of rumor diffusion and extend it to consider more general networks

    Going Beyond Counting First Authors in Author Co-citation Analysis

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    The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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