Gosselin, Pierre and Lotz, Aïleen and Wambst, Marc (2017): A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous 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 agent's complexity. The formalism does not seek to aggregate agents: it rather replaces the standard optimization approach by a probabilistic description of the agents' behaviors and of the whole system. 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 timedependent probability distribution centered around its utility optimum.
The whole system of agents is thus defined by a composite probability depending on time, agents' interactions, relations of strategic dominations, agents' information sets and expectations. This setting allows for heterogeneous agents with different utility functions, strategic domination relations, heterogeneity of information, etc.
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 the standard optimization, such a description markedly eases the treatment of a system with a 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, although approximate, treatment of the system. This field theory does not model an aggregation of microeconomic systems in the usual sense, but rather describes an environment of a large number of interacting agents. From this description, various phases or equilibria may be retrieved, as well as the individual agents' behaviors, along with their interaction with the environment. This environment does not necessarily have a unique or stable equilibrium and allows to reconstruct aggregate quantities without reducing the system to mere relations between aggregates.
For illustrative purposes, this paper studies several economic models with a large number of agents, some presenting various phases. These are models of consumer/producer agents facing binding constraints, business cycle models, and psychoeconomic models of interacting and possibly strategic agents.
Item Type:  MPRA Paper 

Original Title:  A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents 
Language:  English 
Keywords:  path integrals; statistical field theory; phase transition; non trivial vacuum; effective action; Green function; correlation functions; business cycle; budget constraint; aggregation; forwardlooking behavior; heterogeneous agents; multiagent model; strategical advantage; interacting agents; psychoeconomic models; integrated structures; emergence. 
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:  79926 
Depositing User:  Aileen Lotz 
Date Deposited:  29 Jun 2017 13:06 
Last Modified:  29 Jun 2017 13:07 
References:  Anirban Chakraborti, Ioane Muni Toke, Marco Patriarca and Frédéric Abergel, 2011: Econophysics review: I. Empirical facts, Quantitative Finance, Vol. 11, No. 7, 9911012. Anirban Chakraborti, Ioane Muni Toke, Marco Patriarca and Frédéric Abergel, 2011: Econophysics review: II. Agentbased models, Quantitative Finance, Vol. 11, No. 7, 10131041. Aïleen Lotz: An Economic Approach to the Self: the Dual Agent, Preprint, 2011. https://mpra.ub.unimuenchen.de/50771/1/MPRA_paper_50771.pdf Pierre Gosselin and Aïleen Lotz: A dynamic model of interactions between conscious and unconscious, Preprint, 2012. https://mpra.ub.unimuenchen.de/36697/1/MPRA_paper_36697.pdf. Pierre Gosselin, Aïleen Lotz, and Marc Wambst: On Apparent Irrational Behavior : Interacting Structures and the Mind, Preprint, 2013. https://hal.archivesouvertes.fr/hal00851309/document Pierre Gosselin, Aïleen Lotz, and Marc Wambst: From Rationality to Irrationality : Dynamic Interacting Structures, IF PREPUB. 2015. https://hal.archivesouvertes.fr/hal01122078/document Kleinert Hagen: 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. Kleinert Hagen: Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets 5th edition, World Scientific, Singapore 2009. Hamilton James D.: Time series analysis. Princeton University Press, 1994. ZinnJustin Jean: Quantum Field Theory and Critical Phenomena, 2nd edition, Oxford Science Publications, 1993. Peskin M. E., Schroeder D. V., An introduction to Quantum Field Theory. AddisonWesley Publishing Company 1995. Romer David: Advanced Macroeconomics, 4th edition. McGrawHill Higher Education, 2011. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/79926 
Available Versions of this Item

A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents. (deposited 03 Jun 2017 08:24)

A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents. (deposited 11 Jun 2017 15:42)

A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents. (deposited 12 Jun 2017 19:51)
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A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents. (deposited 12 Jun 2017 19:51)

A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents. (deposited 11 Jun 2017 15:42)