Communication and optimal hierarchical networks

We study a general and simple model for communication processes. In the model, agents in a network (in particular, an organization) interchange information packets following simple rules that take into account the limited capability of the agents to deal with packets and the cost associated to the existence of open communication channels. Due to the limitation in the capability, the network collapses under certain conditions. We focus on when the collapse occurs for hierarchical networks and also on the influence of the flatness or steepness of the structure. We find that the need for hierarchy is related to the existence of costly connections.Comment: 7 pages, 2 figures. NATO ARW on Econophysic

Adaptive simulation using mode identification

Adaptive simulation using modal clustering and method of potential function

Statistical Dynamics of Religions and Adherents

Religiosity is one of the most important sociological aspects of populations. All religions may evolve in their beliefs and adapt to the society developments. A religion is a social variable, like a language or wealth, to be studied like any other organizational parameter. Several questions can be raised, as considered in this study: e.g. (i) from a ``macroscopic'' point of view : How many religions exist at a given time? (ii) from a ``microscopic'' view point: How many adherents belong to one religion? Does the number of adherents increase or not, and how? No need to say that if quantitative answers and mathematical laws are found, agent based models can be imagined to describe such non-equilibrium processes. It is found that empirical laws can be deduced and related to preferential attachment processes, like on evolving network; we propose two different algorithmic models reproducing as well the data. Moreover, a population growth-death equation is shown to be a plausible modeling of evolution dynamics in a continuous time framework. Differences with language dynamic competition is emphasized.Comment: submitted to EP

Prisoner's Dilemma cellular automata revisited: evolution of cooperation under environmental pressure

We propose an extension of the evolutionary Prisoner's Dilemma cellular automata, introduced by Nowak and May \cite{nm92}, in which the pressure of the environment is taken into account. This is implemented by requiring that individuals need to collect a minimum score $U_{min}$, representing indispensable resources (nutrients, energy, money, etc.) to prosper in this environment. So the agents, instead of evolving just by adopting the behaviour of the most successful neighbour (who got $U^{msn}$), also take into account if $U^{msn}$ is above or below the threshold $U_{min}$. If $U^{msn}<U_{min}$ an individual has a probability of adopting the opposite behaviour from the one used by its most successful neighbour. This modification allows the evolution of cooperation for payoffs for which defection was the rule (as it happens, for example, when the sucker's payoff is much worse than the punishment for mutual defection). We also analyse a more sophisticated version of this model in which the selective rule is supplemented with a "win-stay, lose-shift" criterion. The cluster structure is analyzed and, for this more complex version we found power-law scaling for a restricted region in the parameter space.Comment: 15 pages, 8 figures; added figures and revised tex

Making new connections towards cooperation in the prisoner's dilemma game

Evolution of cooperation in the prisoner's dilemma game is studied where initially all players are linked via a regular graph, having four neighbors each. Simultaneously with the strategy evolution, players are allowed to make new connections and thus permanently extend their neighborhoods, provided they have been successful in passing their strategy to the opponents. We show that this simple coevolutionary rule shifts the survival barrier of cooperators towards high temptations to defect and results in highly heterogeneous interaction networks with an exponential fit best characterizing their degree distributions. In particular, there exist an optimal maximal degree for the promotion of cooperation, warranting the best exchange of information between influential players.Comment: 6 two-column pages, 7 figures; accepted for publication in Europhysics Letter

Distinguishing the opponents in the prisoner dilemma in well-mixed populations

Here we study the effects of adopting different strategies against different opponent instead of adopting the same strategy against all of them in the prisoner dilemma structured in well-mixed populations. We consider an evolutionary process in which strategies that provide reproductive success are imitated and players replace one of their worst interactions by the new one. We set individuals in a well-mixed population so that network reciprocity effect is excluded and we analyze both synchronous and asynchronous updates. As a consequence of the replacement rule, we show that mutual cooperation is never destroyed and the initial fraction of mutual cooperation is a lower bound for the level of cooperation. We show by simulation and mean-field analysis that for synchronous update cooperation dominates while for asynchronous update only cooperations associated to the initial mutual cooperations are maintained. As a side effect of the replacement rule, an "implicit punishment" mechanism comes up in a way that exploitations are always neutralized providing evolutionary stability for cooperation

Nonequilibrium phase transition in a model for social influence

We present extensive numerical simulations of the Axelrod's model for social influence, aimed at understanding the formation of cultural domains. This is a nonequilibrium model with short range interactions and a remarkably rich dynamical behavior. We study the phase diagram of the model and uncover a nonequilibrium phase transition separating an ordered (culturally polarized) phase from a disordered (culturally fragmented) one. The nature of the phase transition can be continuous or discontinuous depending on the model parameters. At the transition, the size of cultural regions is power-law distributed.Comment: 5 pages, 4 figure

Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game

Strategy changes are an essential part of evolutionary games. Here we introduce a simple rule that, depending on the value of a single parameter $w$, influences the selection of players that are considered as potential sources of the new strategy. For positive $w$ players with high payoffs will be considered more likely, while for negative $w$ the opposite holds. Setting $w$ equal to zero returns the frequently adopted random selection of the opponent. We find that increasing the probability of adopting the strategy from the fittest player within reach, i.e. setting $w$ positive, promotes the evolution of cooperation. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction network. Since the evolution to widespread defection is tightly associated with cooperators having a lower fitness than defectors, the fact that positive values of $w$ facilitate cooperation is quite surprising. We show that the results can be explained by means of a negative feedback effect that increases the vulnerability of defectors although initially increasing their survivability. Moreover, we demonstrate that the introduction of $w$ effectively alters the interaction network and thus also the impact of uncertainty by strategy adoptions on the evolution of cooperation.Comment: 7 two-column pages, 5 figures; accepted for publication in Physical Review