We present examples of agent-based and stochastic models of competition and business processes in economics and finance. We start from as simple as possible models, which have microscopic, agent-based, versions and macroscopic treatment in behavior. Microscopic and macroscopic versions of herding model proposed by Kirman and Bass diffusion of new products are considered in this contribution as two basic ideas. Further we demonstrate that general herding behavior can be considered as a background of nonlinear stochastic model of financial fluctuations.
Some might argue that agent-based models need not to be analytically tractable and in fact that agent-based models are best suited to model phenomena, which is too complex to be analytically described @cite_87 . But the recent developments show that many groups attempt to build a bridge between microscopic and macroscopic models. Possibly one of the earliest attempts to do so started from not so realistic, nor tractable El Farol bar problem'' @cite_16 . This simple model quickly became known as the Minority Game @cite_3 and over few years received analytic treatment @cite_60 . Another prominent simple agent-based model was created by Kirman @cite_8 , which gained broader attention only very recently @cite_38 @cite_85 @cite_2 @cite_57 . In @cite_75 we have given this model and extended analytical treatment and have shown that this model coincides with some prominent macroscopic, namely stochastic, models of the financial markets (see Section of this work for more details). Another interesting development was made by following the aforementioned Bornholdt's spin model, which has recently received an analytical treatment via mean-field formalism @cite_4 .
@cite_38 @cite_4 @cite_60 @cite_8 @cite_87 @cite_85 @cite_3 @cite_57 @cite_2 @cite_16 @cite_75
2761043131 2953060309 2151287978 2097397187
Agent-based modeling of zapping behavior of viewers, television commercial allocation, and advertisement markets by Hiroyuki Kyan and Jun-ichi Inoue.- Agent based modeling of Housing asset bubble: A simple utility function based investigation by Kausik Gangopadhyay and Kousik Guhathakurta.- Urn model-based adaptive Multi-arm clinical trials: A stochastic approximation approach by Sophie Laruelle and Gilles Pages.- Logistic modeling of a Religious Sect features by Marcel Ausloos.- Characterizing financial crisis by means of the three states random field Ising model by Mitsuaki Murota and Jun-ichi Inoue.- Themes and applications of kinetic exchange models: Redux by Asim Ghosh, Anindya S. Chakrabarti, Anjan Kumar Chandra and Anirban Chakraborti.- Kinetic exchange opinion model: solution in the single parameter map limit by Krishanu Roy Chowdhury, Asim Ghosh, Soumyajyoti Biswas and Bikas K. Chakrabarti.- An overview of the new frontiers of Economic Complexity by Matthieu Cristelli, Andrea Tacchella, Luciano Pietronero.- Jan Tinbergen's legacy for economic networks: from the gravity model to quantum statistics by Tiziano Squartini and Diego Garlaschelli.- A macroscopic order of consumer demand due to heterogenous consumer behaviors on Japanese household demand tested by the random matrix theory by Yuji Aruka,Yuichi Kichikawa and Hiroshi Iyetomi.- Uncovering the network structure of the world currency market: Cross-correlations in the fluctuations of daily exchange rates by Sitabhra Sinha and Uday Kovur.- Systemic risk in Japanese credit network by Hideaki Aoyama.- Pricing of goods with Bandwagon properties: The curse of coordination by Mirta B. Gordon, Jean-Pierre Nadal, Denis Phan and Viktoriya Semeshenko.- Evolution of Econophysics by Kishore C. Dash.- Econophysics and sociophysics: Problems and prospects by Asim Ghosh and Anindya S. Chakrabarti.- A discussion on Econophysics by Hideaki Aoyama. Schelling's model of segregation looks to explain the way in which particles or agents of two types may come to arrange themselves spatially into configurations consisting of large homogeneous clusters, i.e. connected regions consisting of only one type. As one of the earliest agent based models studied by economists and perhaps the most famous model of self-organising behaviour, it also has direct links to areas at the interface between computer science and statistical mechanics, such as the Ising model and the study of contagion and cascading phenomena in networks. While the model has been extensively studied it has largely resisted rigorous analysis, prior results from the literature generally pertaining to variants of the model which are tweaked so as to be amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. In BK , Brandt, Immorlica, Kamath and Kleinberg provided the first rigorous analysis of the unperturbed model, for a specific set of input parameters. Here we provide a rigorous analysis of the model's behaviour much more generally and establish some surprising forms of threshold behaviour, notably the existence of situations where an level of intolerance for neighbouring agents of opposite type leads almost certainly to segregation. A growing body of recent literature allows for heterogenous trading strategies and limited rationality of agents in behavioral models of financial markets. More and more, this literature has been concerned with the explanation of some of the stylized facts of financial markets. It now seems that some previously mysterious time-series characteristics like fat tails of returns and temporal dependence of volatility can be observed in many of these models as macroscopic patterns resulting from the interaction among different groups of speculative traders. However, most of the available evidence stems from simulation studies of relatively complicated models which do not allow for analytical solutions. In this paper, this line of research is supplemented by analytical solutions of a simple variant of the seminal herding model introduced by Kirman [1993]. Embedding the herding framework into a simple equilibrium asset pricing model, we are able to derive closed-form solutions for the time-variation of higher moments as well as related quantities of interest enabling us to spell out under what circumstances the model gives rise to realistic behavior of the resulting time series We introduce a minimal Agent Based Model for financial markets to understand the nature and Self-Organization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random Walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The Stylized Facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effect which, however, can occur at different time scales. We propose a new mechanism for the Self-Organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represent a crucial element for this state of Self-Organized-Intermittency. The model can be easily generalized to consider more realistic variants.