Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1810.07178

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

Aïleen Lotz·Pierre Gosselin·Marc Wambst
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

econ.GNcond-mat.stat-mechq-fin.ECq-fin.GN

Keep this discovery

BibTeXRIS

Aïleen Lotz, Pierre Gosselin, Marc Wambst. 2018-10-16. A Path Integral Approach to Business Cycle Models with Large Number of Agents. https://arxiv.org/abs/1810.07178

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reducing Prescription Errors Through Information Intervention: A Field Experiment in Healthcare Operations

Drug-drug interaction (DDI) errors pose serious risks to patient safety. Existing decision-support systems often require physicians to respond to alerts, disrupting workflows and contributing to high override rates. We examine whether a non-mandatory information intervention can reduce DDI errors and foster learning. Using a randomized field experiment with India's largest electronic medical record platform, we analyze 2.81 million prescriptions from 1,700 physicians using a difference-in-differences design. Treatment physicians received real-time information highlighting DDI errors without being required to respond, while control physicians received no such information. The intervention reduced DDI errors by 8.6%, corresponding to an estimated US$4.8 million in annual hospitalization cost savings and approximately 134 lives potentially saved. We identify two mechanisms: reactive correction, whereby physicians remove errors after they are flagged, and proactive learning, whereby they avoid errors before alerts occur. While early reductions are driven primarily by correction, physicians increasingly avoid errors over time. They also become less likely to repeat previously flagged errors and reduce new errors, suggesting that learning generalizes beyond specific drug pairs. The effects are consistent across physician types and do not compromise productivity or care quality. Our findings show that non-mandatory information interventions can improve patient safety through both immediate error correction and persistent, generalizable learning.

econ.GN↗
arXiv2026

How an Economy Shrinks in Space: Concavity-on-Jobs and Upward Consolidation under Demographic Decline

When a country's population declines, the aggregate economy appears to contract on the intensive margin: industrial diversity intact, every industry a little smaller. At the regional level, contraction is uneven and takes the extensive form: entire industries disappear, one after another. The relevant unit is the city: industries are nested by size - the hierarchy property of industrial location - each viable only above a minimum population. Necessity industries' thresholds bunch at the low end, so a city's industry count - and its jobs - is sharply concave in size (concavity on jobs). A modest loss pushes a small city below many thresholds at once; a large core sheds a few specialized industries, one at a time. Lost industries consolidate upward to the next city large enough to host them; for the worker it means a step down to a lower-paid local job. To recover that income, workers move up to the apex - the only city hosting the full industry range. Studying Japan - two decades ahead of the OECD, Tokyo at its apex - with worker-level panel data on the young workers who carry the migration, a wage regression in real, housing-inclusive wages identifies a Tokyo-bound migration incentive that varies by origin, following concavity on jobs.

econ.GN↗
arXiv2026

Do wind and solar curtail at negative electricity prices? Incentives and evidence across two decades of German renewable support schemes

In many power systems, wind and solar generation increasingly often exceeds electricity demand. Curtailing renewable generation in those hours matters both for prices and for the physical stability of the grid. Turning off wind turbines and solar panels is technically easier than ramping down a large power station, yet support schemes often give renewables an economic incentive to keep producing at negative prices. This paper studies wind and solar energy in Germany. For each cohort of generators it estimates, hour by hour, the incentive implied by two decades of support policy. It then sets those incentives against observed behavior, using a new estimate of market-based curtailment built from reanalysis weather data. I find that in 2025, at prices below -50 EUR/MWh, almost all wind generators had an incentive to stop producing, but only half of them did. Solar is the opposite case: nearly two thirds of the potential had no incentive to curtail at all, mostly because it receives a feed-in tariff that shields it from wholesale prices. Of the exposed remainder, just over a fifth cut production. Low exposure and response rates inflate subsidy payments and make the power system harder to operate safely. I conclude that a further expansion of wind and solar requires them to respond to price signals.

econ.GN↗