Same Mean Lag, Different Stability: Periodic Implementation in Adaptive Competition
Abstract
Can two implementation processes with the same mean lag give opposite stability predictions for adaptive competition? We show that they can, and quantify the discrepancy. The motivating problem is technological coadaptation: decisions are revised while earlier changes are still being implemented and the competing system continues to change. Configuration updates in adaptive cyber defence and activation of revised algorithmic trading strategies provide concrete settings for this modelling question. A coupled replicator--mutator model separates intended portfolios from those actually in use. Near a uniform interior equilibrium, the interaction geometry determines the feedback branches; under strict antagonism, the largest singular value identifies the first unstable mode. For continuous implementation, hard observation and implementation lags enter through one delay budget. Replacing one smooth implementation filter by periodic partial updates, with zero hard lags and a uniform eligibility-phase calibration, preserves the mean waiting time but lowers the first gain boundary by an explicit positive quadratic correction for short release periods. A reproducible three-strategy benchmark exhibits decay under the continuous model and growth under periodic implementation at the same mean lag and interaction gain. Balanced performance observables can also understate the underlying portfolio oscillations. The results identify a concrete failure of mean-only timing descriptions and provide a benchmark for modelling adaptation and implementation separately.
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BibTeX
@misc{omelchenko2026same,
title = {{Same Mean Lag, Different Stability: Periodic Implementation in Adaptive Competition}},
author = {Alexander Omelchenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.00227},
eprint = {2607.00227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.00227},
}
RIS
TY - UNPB
TI - Same Mean Lag, Different Stability: Periodic Implementation in Adaptive Competition
AU - Alexander Omelchenko
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2607.00227
UR - https://arxiv.org/abs/2607.00227
AB - Can two implementation processes with the same mean lag give opposite stability predictions for adaptive competition? We show that they can, and quantify the discrepancy. The motivating problem is technological coadaptation: decisions are revised while earlier changes are still being implemented and the competing system continues to change. Configuration updates in adaptive cyber defence and activation of revised algorithmic trading strategies provide concrete settings for this modelling question. A coupled replicator--mutator model separates intended portfolios from those actually in use. Near a uniform interior equilibrium, the interaction geometry determines the feedback branches; under strict antagonism, the largest singular value identifies the first unstable mode. For continuous implementation, hard observation and implementation lags enter through one delay budget. Replacing one smooth implementation filter by periodic partial updates, with zero hard lags and a uniform eligibility-phase calibration, preserves the mean waiting time but lowers the first gain boundary by an explicit positive quadratic correction for short release periods. A reproducible three-strategy benchmark exhibits decay under the continuous model and growth under periodic implementation at the same mean lag and interaction gain. Balanced performance observables can also understate the underlying portfolio oscillations. The results identify a concrete failure of mean-only timing descriptions and provide a benchmark for modelling adaptation and implementation separately.
ER -