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A Path Integral Approach to Business Cycle Models with Large Number of Agents

Author

Listed:
  • Aileen Lotz
  • Pierre Gosselin
  • Marc Wambst

    (IRMA)

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.

Suggested Citation

  • Aileen Lotz & Pierre Gosselin & Marc Wambst, 2018. "A Path Integral Approach to Business Cycle Models with Large Number of Agents," Papers 1810.07178, arXiv.org.
    • Handle: RePEc:arx:papers:1810.07178
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    References listed on IDEAS

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    1. A. Chakraborti & I. Muni-Toke & M. Patriarca & F. Abergel, 2011. "Econophysics Review : II. Agent-based models," Post-Print hal-03332946, HAL.
    2. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
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    6. Pierre Gosselin & Aïleen Lotz & Marc Wambst, 2015. "From Rationality to Irrationality : Dynamic Interacting Structures," Working Papers hal-01122078, HAL.
    7. Lotz, Aïleen, 2011. "An Economic Approach to the Self : the Dual Agent," MPRA Paper 50771, University Library of Munich, Germany.
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    12. repec:hal:spmain:info:hdl:2441/53r60a8s3kup1vc9l564igg8g is not listed on IDEAS
    13. repec:hal:wpspec:info:hdl:2441/53r60a8s3kup1vc9l564igg8g is not listed on IDEAS
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    Cited by:

    1. Pierre Gosselin & Aïleen Lotz & Marc Wambst, 2021. "A statistical field approach to capital accumulation," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(4), pages 817-908, October.
    2. Lotz, Aïleen, 2011. "An Economic Approach to the Self : the Dual Agent," MPRA Paper 30043, University Library of Munich, Germany.
    3. Pierre Gosselin & Aïleen Lotz & Marc Wambst, 2019. "A Statistical Field Approach to Capital Accumulation," Working Papers hal-02280634, HAL.

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    More about this item

    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

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