Using deterministic tourist walk as a small-world metric on Watts-Strogatz networks

The Watts-Strogatz model (WS) has been demonstrated to effectively describe real-world networks due to its ability to reproduce the small-world properties commonly observed in a variety of systems, including social networks, computer networks, biochemical reactions, and neural networks. As the presence of small-world properties is a prevalent characteristic in many real-world networks, the measurement of "small-worldness" has become a crucial metric in the field of network science, leading to the development of various methods for its assessment over the past two decades. In contrast, the deterministic tourist walk (DTW) method has emerged as a prominent technique for texture analysis and network classification. In this paper, we propose the use of a modified version of the DTW method to classify networks into three categories: regular networks, random networks, and small-world networks. Additionally, we construct a small-world metric, denoted by the coefficient $\chi$, from the DTW method. Results indicate that the proposed method demonstrates excellent performance in the task of network classification, achieving over $90\%$ accuracy. Furthermore, the results obtained using the coefficient $\chi$ on real-world networks provide evidence that the proposed method effectively serves as a satisfactory small-world metric.Comment: 9 pages, 4 figure

Spatial interactions in agent-based modeling

Agent Based Modeling (ABM) has become a widespread approach to model complex interactions. In this chapter after briefly summarizing some features of ABM the different approaches in modeling spatial interactions are discussed. It is stressed that agents can interact either indirectly through a shared environment and/or directly with each other. In such an approach, higher-order variables such as commodity prices, population dynamics or even institutions, are not exogenously specified but instead are seen as the results of interactions. It is highlighted in the chapter that the understanding of patterns emerging from such spatial interaction between agents is a key problem as much as their description through analytical or simulation means. The chapter reviews different approaches for modeling agents' behavior, taking into account either explicit spatial (lattice based) structures or networks. Some emphasis is placed on recent ABM as applied to the description of the dynamics of the geographical distribution of economic activities, - out of equilibrium. The Eurace@Unibi Model, an agent-based macroeconomic model with spatial structure, is used to illustrate the potential of such an approach for spatial policy analysis.Comment: 26 pages, 5 figures, 105 references; a chapter prepared for the book "Complexity and Geographical Economics - Topics and Tools", P. Commendatore, S.S. Kayam and I. Kubin, Eds. (Springer, in press, 2014

Influence of space and time dimensions in multi-agent models of the free-riding collective phenomenon

This report discusses how considering spatial and temporal dimensions at the modelling stage may have an influence on the outcome of the study in collective phenomena. We compared different models built on the same initial individual behaviour hypothesis of one collective phenomenon known as ''free-riding'' (that can be observed in peer-to-peer file sharing networks). % This can be present in peer-to-peer file sharing networks. Those models are conceived to answer questions related to the convergence and stabilization of the sharing behaviour of the users in those networks, where the non-cooperative behaviour of a subset of users may lead to the collapse of the entire network. Building up from this same individual behaviour, we study one global analytical model and four multi-agent models, the latter ones adding space and time dimensions, which are rarely seen in the literature discussing aggregated models of the collective phenomenon in question. After discussing the \textit{a priori} and the experimental conditions under which the models are equivalent, we show that the same individual decision algorithm can lead to contradictory information and results

Multi-agent Systems as Discrete Dynamical Systems: Influences and Reactions as a Modelling Principle

Finding adequate descriptions of multi-agent systems is a central issue for modelling collective dynamics. We propose a mathematical description of multi-agent systems as discrete dynamical systems. The ground of our proposition is the influence-reaction method of Ferber and Müller. The key idea is that agents should never act directly on other components of the system (agents or environment) but release influences which are then combined to update the state of the system. We propose a method which decomposes the definitions of multi-agent system into six parts. We illustrate our method on the multi-Turmite model, also known as the multiple Langton's ants model. We exhibit two formulations of this model, which we study with three different simulation schemes. We show that for the same formulation, and the same initial conditions, the use of different simulation schemes may lead to qualitatively different evolutions of the system. As a positive spin-off of this study, we exhibit new phenomena of the multi-Turmite model such as deadlocks or gliders

L'analyse économique des normes : représentation et traitement des interactions dans les modèles de simulation

L'ensemble des travaux que l'on regroupe sous la même dénomination d'"analyse économique des normes" sont relativement dispersés. Ce qui fait leur point commun est qu'ils se revendiquent de l'individualisme méthodologique et qu'ils donnent lieu à des modélisations de l'interaction entre les acteurs. La présentation qui en est faite ici vise moins la rédaction d'un "survey" que l'indication des hypothèses principales et des options de recherche choisies. Après avoir précisé les termes d'une convergence de travaux récents vers une analyse économique des normes, on se concentre sur deux grands axes de ces approches : les démarches "analytiques" qui reposent sur des modèles stochastiques, et les simulations multi-agents.analyse économique ; norme ; modèle ; simulation

On the disequilibrium dynamics of sequential monetary economies

The purpose of this paper is to study the dynamic behavior of a sequential monetary exchange economy. Transactions take place sequentially against non-equilibrium prices, there is quantity rationing, and credit or cash are the only means of exchange. Agents have optimistic or pes- simistic expectations about quantity constraints that represent their beliefs about future trading opportunities. In the credit model the agents incur debts along the transition path towards equilibrium, while in the cash-in-advance model convergence takes place without the occurrence of any debts or claims. The credit mechanism is shown to act as a 'soft' correction mechanism on credit fluctuations, while the cash-in-advance constraint acts as a 'hard' negative feedback effect driving the prices back towards a neighborhood of a monetary cash-in-advance equilibrium

Política monetária óptima e o processo de formação e difusão de expectativas heterogéneas

Classificação JEL: E10, E32, D83, D84, D85Propomos, no presente trabalho, um modelo macroeconómico behaviorista enquadrado pela metodologia e conceitos dos sistemas multiagentes, constituído por um conjunto de agentes económicos autónomos que comunicam entre si, actuando sobre o espaço simbólico e reagindo quer ao espaço em que estão enquadrados quer à interacção com os restantes agentes. O modelo proposto assume que os agentes económicos são detentores de capacidades cognitivas limitadas (sendo no entanto racionais) que condicionam a sua capacidade de percepcionar o mundo. Fruto desta caracterização do comportamento dos agentes económicos, assumimos que as narrativas ou expectativas sobre o mundo por eles criadas resultam, em grande medida, da confrontação com as representações do mundo realizadas por outros agentes. O processo modelado de formação e difusão de expectativas ou narrativas é, neste contexto, um processo distribuído, no qual a dinâmica das expectativas é a dinâmica de um processo distribuído de redes complexas adaptativas. Com este modelo, quisemos perceber qual o impacto de diferentes mecanismos de interacção e confrontação de representações do mundo na determinação da política monetária óptima seguida pelo banco central. Aquilo que concluímos é que não se pode negligenciar que as propriedades macro (topologia) de uma rede exógena de agentes possuem uma influência causal no processo de emergência micro para macro. Ou seja, não podemos negligenciar a topologia de interacção dos agentes económicos aquando da determinação da política monetária óptima.In this paper we propose a behaviorist macroeconomic model framed by the multi-agent systems methodology and concepts and consisting of a set of autonomous economic agents which communicate with each other, act on the symbolic space and react both to the space in which they exist and to the interaction with the other agents. The proposed model assumes that economic agents have limited cognitive abilities (although being rational) that condition their ability to perceive the world. As a result of this characterization of the economic agents’ behavior, we assume that the narratives or expectations created derive in large measure from confronting their own world representations with the ones made by other agents. The process of formation and diffusion of expectations or narratives is then modeled as a distributed process, in which the dynamics of expectations is the dynamics of a distributed process of complex adaptive networks. Through this model, we sought to understand the impact of different mechanisms of interaction and confrontation of representations of the world in determining the optimal monetary policy followed by the central bank. What we conclude is that one cannot overlook that the macro properties (topology) of a network of exogenous agents have a causal influence on the process of micro to macro emergence. That is, we cannot neglect the topology of interaction of economic agents when determining optimal monetary policy