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.
Our work in the modeling of complex social and economic systems has begun from the applications of nonlinear stochastic differential equations (abbr. SDE) seeking reproduce statistics of financial market data. The proposed class of equations has power law statistics evidently very similar to the ones observed in the empirical data. As all of this work (for broad review see @cite_12 ) was done by relying on the macroscopic phenomenological reasoning, we are now motivated to find the microscopic reasoning for the proposed equations. The development of the macroscopic treatments for the well established agent-based models appears to be the most consistent approach, as the movement in the opposite direction seems to be very complex and ambiguitious task. Thus we decided that we should select the simple agent-based models, which would have an expected macroscopic description. In this contribution we present a few examples of the agent-based modeling, based on the Kirman's model, in the business and finance while showing that the examples have useful and informative macroscopic treatments.
@cite_12
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We extend Kirman’s model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman’s agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics. 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. The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABMs) can reproduce. We propose a methodology, inspired by statistical physics, that characterizes a model through its “phase diagram” in the space of parameters. Our first motivation is to understand the large macro-economic fluctuations observed in the “Mark I” ABM devised by Delli Gatti and collaborators. In this regard, our major finding is the generic existence of a phase transition between a “good economy” where unemployment is low, and a “bad economy” where unemployment is high. We then introduce a simpler framework that allows us to show that this transition is robust against many modifications of the model, and is generically induced by an asymmetry between the rate of hiring and the rate of firing of the firms. The unemployment level remains small until a tipping point, beyond which the economy suddenly collapses. If the parameters are such that the system is close to this transition, any small fluctuation is amplified as the system jumps between the two equilibria. We have explored several natural extensions of the model. One is to introduce a bankruptcy threshold, limiting the firms maximum level of debt-to-sales ratio. This leads to a rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. We also introduce simple wage policies. This leads to inflation (in the “good” phase) or deflation (in the “bad” phase), but leaves the overall phase diagram of the model essentially unchanged. We have also explored the effect of simple monetary policies that attempt to contain rising unemployment and defang crises. We end the paper with general comments on the usefulness of ABMs to model macroeconomic phenomena, in particular in view of the time needed to reach a steady state that raises the issue of ergodicity in these models. This paper reports statistical analyses performed on simulated data from a stochastic multi-agent model of speculative behaviour in a financial market. The price dynamics resulting from this artificial market process exhibits the same type of scaling laws as do empirical data from stock markets and foreign exchange markets: (i) one observes scaling in the probability distribution of relative price changes with a Pareto exponent around 2.6, (ii) volatility shows significant long-range correlation with a self-similarity parameter H around 0.85. This happens although we assume that news about the intrinsic or fundamental value of the asset follows a white noise process and, hence, incorporation of news about fundamental factors is insufficient to explain either of the characteristics (i) or (ii). As a consequence, in our model, the main stylised facts of financial data originate from the working of the market itself and one need not resort to scaling in unobservable extraneous signals as an explanation of the source of scaling in financial prices. The emergence of power laws can be explained by the existence of a critical state which is repeatedly approached in the course of the system's development.