Scale and Staging in Competitive Automation: Demand Externalities with State-Dependent Reabsorption
Antonios Frangotsinos · Zenodo (CERN European Organization for Nuclear Research) · 16 Oct 2026
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Abstract
Abstract Falk and Tsoukalas show that competitive firms may choose an excessive automation endpoint because each firm captures its own labour-cost saving while internalising only part of the product-demand loss generated by worker displacement. This paper studies a second choice margin: the temporal staging of displacement. We first establish a full-horizon null. Under stationary exogenous recovery, all finite displacement paths reaching the same automation endpoint generate identical complete-lifetime unresolved exposure, despite potentially different peaks. Timing becomes consequential only when the transition changes subsequent recovery. We introduce state-dependent reabsorption and show that, under an increasing, concave total service flow with a stable residual process, an undivided displacement batch weakly maximises complete-tail exposure; genuine splitting is strictly beneficial under strict residual convexity. A declining individual recovery hazard alone is insufficient. At a fixed endpoint, partial private internalisation produces a signed staging distortion: excessive front-loading where marginal common timing cost is positive and excessive delay where it is negative. We then solve the joint endpoint-staging problem, establish unique private and cooperative targets, and derive a target-specific two-rate correction with a controlled return to the source model. The analysis is theoretical and uncalibrated; it does not establish that current AI adoption is excessive or prescribe numerical policy rates. Research status Working paper, version 0.1 (September 2026). Not peer reviewed. Independent technical review and empirical validation have not been completed. AI assistance and research transparency OpenAI ChatGPT was used substantively during the research and manuscript-development process, including theoretical exploration, mathematical formulation, proof and counterexample analysis, literature exploration, drafting and editing, and the development and execu
About this publication
Preprint. A preprint — posted publicly before or without journal peer review; findings may still be revised.
- Published
- 2026 (recently)
- Citations
- 3 (OpenAlex)
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3 citations — 100th percentile among the 166 indexed papers from 2026 in this collection. Citation counts favor older papers; this compares only same-year papers here, not the whole literature.
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