1 Introduction
Common-pool resource theory (Hardin 1968; Ostrom 1990) frames the management of shared resources as a problem of who decides what. The polycentric extension of that program (Ostrom 2010; Carlisle and Gruby 2019; Heikkila et al. 2018) recognises that real-world commons are not governed by a single authority but by multiple overlapping decision centres that interact through cooperation, competition and conflict resolution. This literature has produced a rich body of empirical and theoretical work on which instruments such arrangements should deploy — caps, levies, sanctions, exclusion — and on the institutional conditions under which they succeed (Heikkila et al. 2018; Morrison et al. 2019). It has said comparatively little, however, about the temporal structure of the signal that a regulator should act upon — specifically, whether it monitors a leading indicator (one that moves before the damage, such as capital accumulation) or a lagging indicator (one that moves after, such as pollution concentration).
In parallel, the past decade has seen a sharp rise in interest in cascading tipping in coupled environmental systems: scenarios in which one subsystem crossing a critical threshold destabilises others linked to it (Lenton et al. 2019; Armstrong McKay et al. 2022; Wunderling et al. 2024). The risk of greatest concern is no longer the isolated collapse of a single tipping element, but the propagation of such transitions across coupled elements — ice sheets, ocean circulation, ecosystems, atmospheric flows. A small but growing literature is now formalising the dynamical anatomy of these cascades, distinguishing two-phase, domino and joint patterns according to how the critical transition propagates from one element to the next (Klose et al. 2021), and characterising the leading-following structure of unidirectionally coupled subsystems where one component drives another (Sinet et al. 2025).
The present paper sits at the intersection of these two literatures and addresses a question neither has framed explicitly: when one jurisdiction’s pollution cascades into its downwind neighbours, which signal inside the emitter should the regulator act upon? We use BDPD (Brunelli 2026) — a deterministic agent-based commons simulator — on a Bardi/Seneca three-variable substrate (Bardi 2017; see also Bardi 2018 for the population-collapse intuition that motivates the framework) to study a minimal leading-following polycentric configuration in the sense of Sinet et al. (2025): an emitter arena A coupled unidirectionally to two downwind arenas B, C through a pollution-import link. In the taxonomy of Klose et al. (2021), the resulting A\(\to\)B/C cascade is a two-phase cascade: the emitter’s Seneca-cliff in capital propagates to the downwind subsystems only after a delay. A real-world analogue, beyond the present model’s scope, is the cross-boundary cascading of nutrient pollution discussed by Ahlström and Cornell (2017) on the global nitrogen and phosphorus cycles.
Within this architecture we ask: which signal inside the emitter should the regulator act upon? Chapter 3 answers this question empirically; Section 4.1 discusses the rate-induced dimension of the result and its relationship to the cascading-tipping taxonomy of Klose et al. (2021).
The contribution is twofold. Substantively, it relocates the policy question from which instrument to which trigger signal and shows that the right signal (capital) is the one already visible to the actors. Methodologically, it offers a minimal stylised substrate in which leading- and lagging-signal governance can be compared head-to-head under structural one-factor-at-a-time (OFAT) robustness, complementing the Monte Carlo robustness ensembles used elsewhere in the cascading-tipping literature (e.g. Wunderling et al. 2021). The remainder of the paper presents the model (Chapter 2), the four results (Chapter 3), the OFAT robustness sweep and its rate-induced boundary (Chapter 4), limitations (Chapter 5), and discussion (Chapter 6).