IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-01549586.html
   My bibliography  Save this paper

A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents

Author

Listed:
  • Pierre Gosselin

    () (IF - Institut Fourier - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes)

  • Aïleen Lotz

    () (Cerca Trova - Université de Lille, Sciences Humaines et Sociales)

  • Marc Wambst

    () (IRMA - Institut de Recherche Mathématique Avancée - UNISTRA - Université de Strasbourg - CNRS - Centre National de la Recherche Scientifique)

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 time-dependent 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 psycho-economic models of interacting and possibly strategic agents.

Suggested Citation

  • Pierre Gosselin & Aïleen Lotz & Marc Wambst, 2017. "A Path Integral Approach to Interacting Economic Systems with Multiple Heterogeneous Agents," Working Papers hal-01549586, HAL.
  • Handle: RePEc:hal:wpaper:hal-01549586
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01549586v2
    as

    Download full text from publisher

    File URL: https://hal.archives-ouvertes.fr/hal-01549586v2/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lotz, Aïleen, 2011. "An Economic Approach to the Self : the Dual Agent," MPRA Paper 30043, University Library of Munich, Germany.
    2. Gosselin, Pierre & Lotz, Aileen & Wambst, Marc, 2013. "On apparent irrational behaviors : interacting structures and the mind," MPRA Paper 44421, University Library of Munich, Germany.
    3. Lotz, Aileen & Gosselin, Pierre, 2012. "A dynamic model of interactions between conscious and unconscious," MPRA Paper 36697, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    effective action; non trivial vacuum; forward-looking behavior; statistical field theory; budget constraint; aggregation; business cycle; path integrals; phase transition; strategical advantage; interacting agents; psycho-economic models; correlation functions; heterogeneous agents; Green function; emergence; integrated structures; multi-agent model;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-01549586. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.