Bayesian updating rules in continuous opinion dynamics models

Here, I investigate the use of Bayesian updating rules applied to modeling how social agents change their minds in the case of continuous opinion models. Given another agent statement about the continuous value of a variable, we will see that interesting dynamics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a uniform distribution. This represents the idea that the other agent might have no idea about what is being talked about. The effect of updating only the first moments of the distribution will be studied, and we will see that this generates results similar to those of the bounded confidence models. On also updating the second moment, several different opinions always survive in the long run, as agents become more stubborn with time. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.

Solving heterogeneous-agent models by projection and perturbation

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solutionof the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible.Matlab programs to solve the model can be downloaded.

Plethysms and interacting boson models

A short review of the plethysm technique aiming to its application in finding branching rules for the reduction of an irreducible representation of a group under the restriction to one of its subgroups is given. The algebraic structure of the interacting boson model and some of its extensions is given together with the branching rules needed to classify their basis states, obtained by the use of plethysms. (C) 2003 American Institute of Physics.

A two-body study of dynamical expansion in the XXZ spin chain and equivalent interacting fermion models

Lo scopo di questa tesi è studiare l'espansione dinamica di due fermioni interagenti in una catena unidimensionale cercando di definire il ruolo degli stati legati durante l'evoluzione temporale del sistema. Lo studio di questo modello viene effettuato a livello analitico tramite la tecnica del Bethe ansatz, che ci fornisce autovalori ed autovettori dell'hamiltoniana, e se ne valutano le proprietà statiche. Particolare attenzione è stata dedicata alle caratteristiche dello spettro al variare dell'interazione tra le due particelle e alle caratteristiche degli autostati. Dalla risoluzione dell'equazione di Bethe vengono ricercate le soluzioni che danno luogo a stati legati delle due particelle e se ne valuta lo spettro energetico in funzione del momento del centro di massa. Si è studiato inoltre l'andamento del numero delle soluzioni, in particolare delle soluzioni che danno luogo ad uno stato legato, al variare della lunghezza della catena e del parametro di interazione. La valutazione delle proprietà dinamiche del modello è stata effettuata tramite l'utilizzo dell'algoritmo t-DMRG (time dependent - Density Matrix Renormalization Group). Questo metodo numerico, che si basa sulla decimazione dello spazio di Hilbert, ci permette di avere accesso a quantità che caratterizzano la dinamica quali la densità e la velocità di espansione. Da queste sono stati estratti i proli dinamici della densità e della velocità di espansione al variare del valore del parametro di interazione.

Localization and mobility-edges in non-interacting fermionic models with disorder

Nel corso degli ultimi decenni la fisica sperimentale ha raggiunto notevoli traguardi nel campo della manipolazione di sistemi di atomi freddi, riaccendendo l'interesse della ricerca su sistemi a lungo studiati teoricamente, ma fino a poco tempo fa impossibili da realizzare sperimentalmente. Questa riaccesa attenzione ha permesso di sfruttare le moderne capacità di calcolo per studiare sistemi quantistici che ancora risultano di difficile realizzazione. In questo contesto si inserisce il rinnovato interesse per i sistemi quantistici monodimensionali caratterizzati dalla presenza di potenziale disordinato. Questi presentano proprietà di trasporto particolari e sotto particolari condizioni sono oggetto di una transizione di localizzazione. La maggior parte degli studi in questo campo rivolgono la loro attenzione a sistemi di particelle fermioniche interagenti. In questo lavoro di tesi analizziamo, invece, sistemi quantistici fermionici non interagenti, mettendo in luce quanto già noto e proponendo strumenti di analisi derivati dallo studio dei sistemi interagenti. In particolare, proponiamo un'analisi statistica dei livelli energetici e poniamo le basi per futuri studi a riguardo.

Opinion dynamics of learning agents: does seeking consensus lead to disagreement?

We study opinion dynamics in a population of interacting adaptive agents voting on a set of issues represented by vectors. We consider agents who can classify issues into one of two categories and can arrive at their opinions using an adaptive algorithm. Adaptation comes from learning and the information for the learning process comes from interacting with other neighboring agents and trying to change the internal state in order to concur with their opinions. The change in the internal state is driven by the information contained in the issue and in the opinion of the other agent. We present results in a simple yet rich context where each agent uses a Boolean perceptron to state their opinion. If the update occurs with information asynchronously exchanged among pairs of agents, then the typical case, if the number of issues is kept small, is the evolution into a society torn by the emergence of factions with extreme opposite beliefs. This occurs even when seeking consensus with agents with opposite opinions. If the number of issues is large, the dynamics becomes trapped, the society does not evolve into factions and a distribution of moderate opinions is observed. The synchronous case is technically simpler and is studied by formulating the problem in terms of differential equations that describe the evolution of order parameters that measure the consensus between pairs of agents. We show that for a large number of issues and unidirectional information flow, global consensus is a fixed point; however, the approach to this consensus is glassy for large societies.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows LIS to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other. (C) 2009 Elsevier B.V. All rights reserved.

Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

Decision‐Making in Public Good Dilemmas: Theory and Agent‐Based Simulation

In many real world contexts individuals find themselves in situations where they have to decide between options of behaviour that serve a collective purpose or behaviours which satisfy one’s private interests, ignoring the collective. In some cases the underlying social dilemma (Dawes, 1980) is solved and we observe collective action (Olson, 1965). In others social mobilisation is unsuccessful. The central topic of social dilemma research is the identification and understanding of mechanisms which yield to the observed cooperation and therefore resolve the social dilemma. It is the purpose of this thesis to contribute this research field for the case of public good dilemmas. To do so, existing work that is relevant to this problem domain is reviewed and a set of mandatory requirements is derived which guide theory and method development of the thesis. In particular, the thesis focusses on dynamic processes of social mobilisation which can foster or inhibit collective action. The basic understanding is that success or failure of the required process of social mobilisation is determined by heterogeneous individual preferences of the members of a providing group, the social structure in which the acting individuals are contained, and the embedding of the individuals in economic, political, biophysical, or other external contexts. To account for these aspects and for the involved dynamics the methodical approach of the thesis is computer simulation, in particular agent-based modelling and simulation of social systems. Particularly conductive are agent models which ground the simulation of human behaviour in suitable psychological theories of action. The thesis develops the action theory HAPPenInGS (Heterogeneous Agents Providing Public Goods) and demonstrates its embedding into different agent-based simulations. The thesis substantiates the particular added value of the methodical approach: Starting out from a theory of individual behaviour, in simulations the emergence of collective patterns of behaviour becomes observable. In addition, the underlying collective dynamics may be scrutinised and assessed by scenario analysis. The results of such experiments reveal insights on processes of social mobilisation which go beyond classical empirical approaches and yield policy recommendations on promising intervention measures in particular.

Aprendizado por Reforço com Valores deInfluência em Sistemas Multi-Agente

We propose a new paradigm for collective learning in multi-agent systems (MAS) as a solution to the problem in which several agents acting over the same environment must learn how to perform tasks, simultaneously, based on feedbacks given by each one of the other agents. We introduce the proposed paradigm in the form of a reinforcement learning algorithm, nominating it as reinforcement learning with influence values. While learning by rewards, each agent evaluates the relation between the current state and/or action executed at this state (actual believe) together with the reward obtained after all agents that are interacting perform their actions. The reward is a result of the interference of others. The agent considers the opinions of all its colleagues in order to attempt to change the values of its states and/or actions. The idea is that the system, as a whole, must reach an equilibrium, where all agents get satisfied with the obtained results. This means that the values of the state/actions pairs match the reward obtained by each agent. This dynamical way of setting the values for states and/or actions makes this new reinforcement learning paradigm the first to include, naturally, the fact that the presence of other agents in the environment turns it a dynamical model. As a direct result, we implicitly include the internal state, the actions and the rewards obtained by all the other agents in the internal state of each agent. This makes our proposal the first complete solution to the conceptual problem that rises when applying reinforcement learning in multi-agent systems, which is caused by the difference existent between the environment and agent models. With basis on the proposed model, we create the IVQ-learning algorithm that is exhaustive tested in repetitive games with two, three and four agents and in stochastic games that need cooperation and in games that need collaboration. This algorithm shows to be a good option for obtaining solutions that guarantee convergence to the Nash optimum equilibrium in cooperative problems. Experiments performed clear shows that the proposed paradigm is theoretical and experimentally superior to the traditional approaches. Yet, with the creation of this new paradigm the set of reinforcement learning applications in MAS grows up. That is, besides the possibility of applying the algorithm in traditional learning problems in MAS, as for example coordination of tasks in multi-robot systems, it is possible to apply reinforcement learning in problems that are essentially collaborative

B2DI a bayesian BDI agent model with causal belief updating based on MSBN

In this paper, we introduce B2DI model that extends BDI model to perform Bayesian inference under uncertainty. For scalability and flexibility purposes, Multiply Sectioned Bayesian Network (MSBN) technology has been selected and adapted to BDI agent reasoning. A belief update mechanism has been defined for agents, whose belief models are connected by public shared beliefs, and the certainty of these beliefs is updated based on MSBN. The classical BDI agent architecture has been extended in order to manage uncertainty using Bayesian reasoning. The resulting extended model, so-called B2DI, proposes a new control loop. The proposed B2DI model has been evaluated in a network fault diagnosis scenario. The evaluation has compared this model with two previously developed agent models. The evaluation has been carried out with a real testbed diagnosis scenario using JADEX. As a result, the proposed model exhibits significant improvements in the cost and time required to carry out a reliable diagnosis.

Agent-based modeling and simulation for the design of the future european Air Traffic Management system: the experience of CASSIOPEIA

The SESAR (Single European Sky ATM Research) program is an ambitious re-search and development initiative to design the future European air traffic man-agement (ATM) system. The study of the behavior of ATM systems using agent-based modeling and simulation tools can help the development of new methods to improve their performance. This paper presents an overview of existing agent-based approaches in air transportation (paying special attention to the challenges that exist for the design of future ATM systems) and, subsequently, describes a new agent-based approach that we proposed in the CASSIOPEIA project, which was developed according to the goals of the SESAR program. In our approach, we use agent models for different ATM stakeholders, and, in contrast to previous work, our solution models new collaborative decision processes for flow traffic management, it uses an intermediate level of abstraction (useful for simulations at larger scales), and was designed to be a practical tool (open and reusable) for the development of different ATM studies. It was successfully applied in three stud-ies related to the design of future ATM systems in Europe.

A nested Petri net framework for modeling and analyzing multi-agent systems

In the past two decades, multi-agent systems (MAS) have emerged as a new paradigm for conceptualizing large and complex distributed software systems. A multi-agent system view provides a natural abstraction for both the structure and the behavior of modern-day software systems. Although there were many conceptual frameworks for using multi-agent systems, there was no well established and widely accepted method for modeling multi-agent systems. This dissertation research addressed the representation and analysis of multi-agent systems based on model-oriented formal methods. The objective was to provide a systematic approach for studying MAS at an early stage of system development to ensure the quality of design. ^ Given that there was no well-defined formal model directly supporting agent-oriented modeling, this study was centered on three main topics: (1) adapting a well-known formal model, predicate transition nets (PrT nets), to support MAS modeling; (2) formulating a modeling methodology to ease the construction of formal MAS models; and (3) developing a technique to support machine analysis of formal MAS models using model checking technology. PrT nets were extended to include the notions of dynamic structure, agent communication and coordination to support agent-oriented modeling. An aspect-oriented technique was developed to address the modularity of agent models and compositionality of incremental analysis. A set of translation rules were defined to systematically translate formal MAS models to concrete models that can be verified through the model checker SPIN (Simple Promela Interpreter). ^ This dissertation presents the framework developed for modeling and analyzing MAS, including a well-defined process model based on nested PrT nets, and a comprehensive methodology to guide the construction and analysis of formal MAS models.^