Gosselin, Pierre and Lotz, Aïleen and Wambst, Marc
(2018):
*A Path Integral Approach to Business Cycle Models with Large Number of Agents.*

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## Abstract

This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces the standard optimization approach by a probabilistic description of both the entire system and agents' behaviors. This is done in two distinct steps. A first step considers an interacting system involving an arbitrary number of agents, where each agent's utility function is subject to unpredictable shocks. In such a setting, individual optimization problems need not be resolved. Each agent is described by a time-dependent probability distribution centered around his utility optimum. The entire system of agents is thus defined by a composite probability depending on time, agents' interactions and forward-looking behaviors. This dynamic system is described by a path integral formalism in an abstract space - the space of the agents' actions - and is very similar to a statistical physics or quantum mechanics system. We show that this description, applied to the space of agents' actions, reduces to the usual optimization results in simple cases. Compared to a standard optimization, such a description markedly eases the treatment of systems with small number of agents. It becomes however useless for a large number of agents. In a second step therefore, we show that for a large number of agents, the previous description is equivalent to a more compact description in terms of field theory. This yields an analytical though approximate treatment of the system. This field theory does not model the aggregation of a microeconomic system in the usual sense. It rather describes an environment of a large number of interacting agents. From this description, various phases or equilibria may be retrieved, along with individual agents' behaviors and their interactions with the environment. For illustrative purposes, this paper studies a Business Cycle model with a large number of agents.

Item Type: | MPRA Paper |
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Original Title: | A Path Integral Approach to Business Cycle Models with Large Number of Agents |

English Title: | A Path Integral Approach to Business Cycle Models with Large Number of Agents |

Language: | English |

Keywords: | path integrals, statistical field theory, business cycle, budget constraint, multi-agent model, interacting agents. |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General E - Macroeconomics and Monetary Economics > E0 - General > E00 - General E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models |

Item ID: | 89488 |

Depositing User: | Aileen Lotz |

Date Deposited: | 24 Oct 2018 06:21 |

Last Modified: | 24 Oct 2018 06:22 |

References: | Abergel F, Chakraborti A, Muni Toke I and Patriarca M(2011) Econophysics review: I. Empirical facts, Quantitative Finance, Vol. 11, No. 7, 991-1012. Abergel F, Chakraborti A, Muni Toke I and Patriarca M (2011) Econophysics review: II. Agent-based models, Quantitative Finance, Vol. 11, No. 7, 1013-1041. Lucas, Robert (1976) "Econometric Policy Evaluation: A Critique". In Brunner, K.; Meltzer, A. The Phillips Curve and Labor Markets. Carnegie-Rochester Conference Series on Public Policy. 1. New York: American Elsevier. pp. 19-46. ISBN 0-444-11007-0. Lotz A (2011) An Economic Approach to the Self: the Dual Agent, Preprint, 2011. https://mpra.ub.uni-muenchen.de/50771/1/MPRA paper 50771.pdf Gosselin P and Lotz A (2012) A dynamic model of interactions between conscious and unconscious, Preprint, 2012. https://mpra.ub.uni-muenchen.de/36697/1/MPRA paper 36697.pdf. Gosselin P, Lotz A, and Wambst M. (2013) On Apparent Irrational Behavior : Interacting Structures and the Mind, Preprint, 2013. https://hal.archives-ouvertes.fr/hal-00851309/document Gosselin P, Lotz A, and Wambst M (2015) From Rationality to Irrationality : Dynamic Interacting Structures, IF PREPUB. 2015. https://hal.archives-ouvertes.fr/hal-01122078/document Gosselin P, Lotz A and Wambst M (2017) A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents. IF PREPUB. 2017. hal-01549586v2 Kleinert H (1989) Gauge Fields in condensed matter Vol. I , Superflow and vortex lines, Disorder Fields, Phase Transitions, Vol. II, Stresses and defects, Differential Geometry, Crystal Melting, World Scientific, Singapore 1989. Gaffard J-L and Napoletano M Editors: Agent-based models and economic policy. Ofce 2012. Jackson M (2010) Social and Economic Networks, Princeton University Press 2010. Kleinert H (2009) Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets 5th edition, World Scientific, Singapore 2009. Hamilton J. D. (1994) Time series analysis. Princeton University Press, 1994. Zinn-Justin J (1993) Quantum Field Theory and Critical Phenomena, 2nd edition, Oxford Science Publications, 1993. Peskin ME, Schroeder DV (1995), An introduction to Quantum Field Theory. Addison-Wesley Publishing Company 1995. Romer, David. Advanced Macroeconomics. New York: McGraw-Hill Companies, 1996 Maurice Obstfeld & Kenneth S. Rogoff, 1996. "Foundations of International Macroeconomics," MIT Press Books, The MIT Press. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/89488 |