1  Introduction

The management of common-pool resources (CPRs) — such as fisheries, forests, and groundwater — is one of the most persistent challenges in socio-ecological systems. Static models of the problem assume that collapse, if it comes, arrives gradually and reversibly enough for institutions to respond. But what happens when it does not — when the transition between sustainable and depleted is discontinuous and irreversible? The classical framing, established by Garrett Hardin, posits that rational individuals will inevitably over-extract from a shared resource, leading to the “Tragedy of the Commons” where private gain conflicts with collective ruin (Hardin 1968). While this model assumes homogeneous actors and costless access, real-world systems are rarely so simple.

Decades of research have revealed that the outcome of CPR management is highly sensitive to heterogeneity, particularly wealth inequality. However, the literature reveals a complex, non-monotonic relationship. Early hypotheses, following Olson (1965), suggested that inequality might actually facilitate collective action, as a single wealthy actor has enough incentive to bear the costs of provision while others free-ride. This view is theoretically supported by Dayton-Johnson and Bardhan (2002), who demonstrated a U-shaped relationship between inequality and resource conservation: efficiency can be achieved under conditions of extreme equality (through universal cooperation) or extreme inequality (through the unilateral action of a rich oligarch), but not in the middle ranges where coordination fails.

Recent experimental and evolutionary models refine this picture. Vasconcelos et al. (2014) show that in climate negotiations modeled as a threshold public goods game, wealth inequality can promote cooperation if the rich compensate for the poor. However, this beneficial dynamic is fragile and collapses under conditions of homophily, which isolates the poor and erodes their willingness to cooperate. Vasconcelos et al. (2015) highlight the efficacy of polycentric governance: smaller, localized agreements are more robust to risk and uncertainty than large-scale global summits. Yoon and Armsworth (2025) demonstrate that voluntary sanctioning mechanisms can restore the sustainability of the commons, expanding the range of inequality levels under which resources can be managed cooperatively. Yet, these institutional solutions implicitly rely on the system remaining within a recoverable state long enough for cooperation or sanctions to take effect (Santos and Pacheco 2011).

A further dimension often overlooked in these models is the temporal asymmetry of resource dynamics. Owusu et al. (2019) observe a “downward spiral of resource overexploitation” in continuous-time experiments, while Pérolat et al. (2017) demonstrate that multi-agent systems evolve through phases of naïvety, tragedy, and maturity. The most formalised model of such asymmetry is the Seneca effect (Bardi 2017): systems tend to grow slowly but collapse rapidly, driven by capital-pollution feedback. Studying how agent composition and wealth inequality interact with this asymmetric collapse dynamic motivates the Bardi ODE engine implemented in the Arena (see §What’s Next: Seneca and Beyond); its systematic sweeps are deferred to future work.

Despite this body of work, an integration gap remains. Wealth inequality, defector dynamics, monitoring imperfection, and temporal asymmetry have each been studied in depth, but seldom in the same agent-based environment, with the same set of parameter knobs, and on two methodologically distinct substrates. The interplay between strategic irreversibility, locally reactive behaviour, and information asymmetry under resource pressure is precisely where collective failures concentrate — and where the literature remains thin.

BDPD (Be Different Play Differential) addresses this gap by providing a unified computational laboratory in which these phenomena can be varied independently and observed jointly. It comprises a multi-agent simulation platform — the Arena — and a tabletop card game, The Forest of Humbaba. The Arena enables exhaustive parametric sweeps over agent composition, resource dynamics, and information structure; the card game translates every Arena mechanism into a tangible object, allowing the same strategic pressures to be encountered in an embodied setting by human or LLM players.

The “differential” in BDPD denotes a design principle: each Arena scenario is characterised by a set of differential equations specifying its resource dynamics — of which the logistic commons (Section 2.1) and the Bardi three-variable model (Bardi 2017) (Appendix A.1) are two instantiations — while the card-game decks are inspired by the same differential structure, mapping ODE-defined agent roles onto physical card mechanics. This is distinct from differential games in the sense of Isaacs (1965).

BDPD is conceived not as a model making claims about any specific real-world system, but as a configurable, open-source testbed: the findings reported here are demonstrations of the laboratory’s capacity to surface counterintuitive dynamics, not definitive proofs about the commons. We address the four research questions below by means of seventeen experimental clusters spanning both substrates: eleven platform sweeps (P1–P11) covering thresholds, structural asymmetries, the epistemic dilemma, and temporal dynamics — each accompanied where relevant by a statistical supplement (B1–B5) probing cliff-edge localisation, slope generalisation, rescue boundary, pure-shock isolation, or cross-sweep inference; and six card-tournament sweeps (CT1–CT6) replicating each platform theme on the stochastic discrete substrate plus one preliminary LLM case study. The research questions are:

The following sections present the BDPD platform and card game (§2), the experimental protocol and the seventeen sweep clusters that probe RQ1–RQ4 (§3), and the integrated interpretation, governance implications, and limitations (§4). Throughout, all experiments are conducted in the absence of communication or sanctioning mechanisms — a deliberate simplification that isolates structural dynamics from governance effects, and defines the baseline against which Ostrom-style interventions can be tested in future sweeps.