A emergência de dilemas sociais e evolução de comportamentos por contágio social em modelos de tráfego veicular

Abstract

This work focuses on uni-dimensional, heterogeneous traffic models. In the first part, we adapted the Nagel and Schreckenberg model (NaSch) to allow overtaking. From the results of analytical calculations and simulations, we show that under certain circumstances overtaking can improve the performance of an individual at a social cost that may hinder the entire population. We analyze and quantify the social dilemma, exploring its causes, and generalize the discussions to other models simulating a more detailed model as an example. In the second part, we analyze general one-dimensional cellular-automata models of vehicular traffic and show that, if the models satisfy the following four simple properties: the interactions are unidirectional; the particles are hard-particles; the dynamics of the particles act as to maximize the velocity or reduce the distances between particles to an optimal distance, and; the system is closed in the sense that there is no exchange of particles with the exterior, then the average velocity in the steady-state of all particles is limited by the average velocity of the slowest particle in the population. Additionally, the net of interactions of the system can be represented by a random, directed graph. Under the evolutionary process of imitation by social contagion, the heterogeneous population is replaced by a homogeneous population composed by the slower strategy in the system, regardless of the initial conditions, initial composition, or the details of the process. Introducing the mutation process as an independent stochastic process, we observe two distinct asymptotic behaviors. If the mutation is the dominant process, the probability distribution of the parameters of any individual is similar to the probability distribution of an m-dimensional random walk where m is the number of parameters. On the other hand, if imitation is the dominant process, the dominating strategies will be particles whose parameters are characteristics of the slower strategy allowed in the space of parameters. Therefore, the inclusion of evolutionary dynamics in these systems transforms the quenched disorders in the space of parameters (as heterogeneous models are generally introduced) in annealed disorders driven to specific regions in that space. We also discuss the similarities of the evolutionary dynamics of these systems with the m-vectors model and observe the similarities among the mentioned limits and unorganized and organized states, respectively. Additional material is added in an appendix regarding investigations on econometric models that awarded us with a publication and the scientific problem we are currently working on. We introduce the Talent versus Luck (TvL) model that attempts to include the roleplay of luck in the success of economic agents in a simple way, putting it in more firm theoretical grounds clarifying its predictions (with special attention to the success of average talent particles) and include the analysis of new predictions like the Matthew effect.