A path integral approach to business cycle models with large number of agents
- PDF / 553,829 Bytes
- 44 Pages / 439.37 x 666.142 pts Page_size
- 7 Downloads / 178 Views
A path integral approach to business cycle models with large number of agents Pierre Gosselin1
· Aïleen Lotz2 · Marc Wambst3
Received: 28 January 2018 / Accepted: 28 December 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 economic variables—and is very similar to a statistical physics or quantum mechanics system. The usual utility optimization of a representative agent is recovered as a particular case. Compared to a standard optimization, such a description 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. Keywords Path integrals · Statistical field theory · Business cycle · Budget constraint · Multi-agent model · Interacting agents
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11403019-00280-3) contains supplementary material, which is available to authorized users. Extended author information available on the last page of the article
123
P. Gosselin et al.
JEL Classification C02 · C60 · E00 · E1
Introduction In many instances, representative agent models have proven unrealistic, lacking both the collective and emerging effects stemming from agents’ interactions. To remedy these pitfalls, various paths have been explored: complex systems, networks, agentbased systems or econophysics. However, agent-based and networks models rely on numerical simulations and may lack m
Data Loading...
