2  The Nested-Arena Substrate at a Glance

This section describes the substrate on which all six vignettes run: what changed relative to a single-arena design, and what the new surfaces afford.

2.1 From single arena to polycentric world

We use polycentric in the Bloomington-school sense (Thiel 2023; Ostrom 1990, 2010): multiple, formally de facto independent but interdependent decision centres provisioning a shared collective good. The nested-arena substrate addresses a structural gap in the ABM-for-SES literature (Lippe et al. 2019; McGinnis and Ostrom 2014; Anderies et al. 2004) — most case-study ABMs do not lift cleanly from village or landscape to regional or world scales.

BDPD\(^1\) (Brunelli 2026a) describes the governance layer that operates on a fully governed single arena: a logistic commons grows at rate \(r\) up to capacity \(K\), players harvest simultaneously each round, pacts are negotiated between players, violations are detected against the pact terms, and an arena-level meta-agent applies sanctions according to a chosen policy. The unit of study there is one commons under one policy.

The nested substrate keeps every one of those mechanisms unchanged and wraps a new object around them. A World holds one or more arenas. Arenas remain the sites of harvest, pact, sanction; the World adds three layers above them:

• Resource Links (Link.type = 'resource'): a one-way per-round outflow \(\alpha \cdot S_{t}^{(\text{src})}\) moves from a source arena’s stock to a target arena’s stock, evaluated in two passes so that link application order does not matter.
• Treaties (World.addTreaty): named objects with payload such as harvest_cap_per_arena_per_round; treaties are observed by meta-agents and enforced through sanctions, but they impose no hard limit on agent decisions. In the normative-MAS sense (Mahmoud et al. 2014), a treaty is a norm with an external enforcer rather than a hard constraint on player choice.
• Meta-agents — arena-level meta-agents (role: 'meta') read full arena state and emit sanction actions inside one arena; world-level meta-agents (World.addMetaAgent) read full world state and can act across arenas. Both register through the same GOVERNANCE_REGISTRY, which accepts new strategies in 30–80 lines.

A fourth ingredient is the exclude perturbation, which migrates a pact-violating player from its home arena to a designated junk arena. The migration preserves wealth and identity but resets pact membership; the receiving arena is otherwise an ordinary arena, so the migrated players continue to interact with whatever institutional structure the junk arena carries (or fails to carry).

Each of these additions has a single load-bearing test that shipped together with it. The remaining empirical question is how these mechanisms behave in combination, and how they behave when the agents under them are LLM players rather than the built-in heuristics for which the single-arena findings were calibrated. The six vignettes — four in the main body, two in the appendices — target precisely those gaps.

2.2 Engine independence

A design constraint inherited from the platform’s earliest release is that no governance mechanism branches on the engineMode of an arena. World, Link, Treaty, exclude, governance registry, observability — none of them imports from engine/<kind>.js. The same substrate therefore applies to logistic commons (used throughout this paper) and to the three-variable Seneca commons (\(R\), \(C\) with hidden pollution \(P\), returned to in Chapter 5). When we discuss a Seneca road in the conclusions, the cost of pursuing it is concentrated in agents and metrics, not in substrate engineering.

2.3 What the substrate does not (yet) do

For honest reading of what follows, three closed doors are worth flagging:

• No cross-arena cheap-talk between arena pacts. Inter-arena communication exists at the meta-agent level but not at the player level.
• Link.type = 'pollution' is implemented since v1.1 and exercised by BDPD\(^3\) (Brunelli 2026b), but is not consumed by the vignettes in this paper; the cross-arena pollution channel is the substrate on which the polycentric Seneca campaign of Road A builds (see Chapter 5).
• No agent persistence across World restarts. World composition is evaluated fresh each run. Long-horizon institutional learning remains an open question.

The vignettes in Chapter 3 work entirely within these boundaries.

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