Mesa Bridge Governance Arc: From Tax to Adaptation to Generalization

Authors: Raeli Savitt Date: 2026-02-27 Framework: SWARM v1.7.0

Abstract

We study the welfare-toxicity tradeoff of externality internalization ($\rho$) in multi-agent AI systems across three progressive experiments totaling 455 simulation runs. In Study 1 (110 runs), we find that $\rho$ alone is a pure welfare tax: it reduces initiator payoffs without lowering toxicity when the acceptance threshold is static. Pairing $\rho$ with an adaptive threshold creates a real governance mechanism, achieving a 34% toxicity reduction at a sweet spot of $\rho \in [0.3, 0.7]$. In Study 2 (165 runs), we introduce learning agents that improve quality in response to rejection, recovering +137% welfare at $\rho = 1.0$ ($d = 11.30$, $p < 0.001$) and Pareto-dominating the adaptive-only regime at every $\rho$ level. In Study 3 (180 runs), we generalize across three game-theoretic structures — Prisoner's Dilemma, Stag Hunt, and Hawk-Dove — demonstrating that learning agents Pareto-dominate across all game types with welfare recovery of 132--159% at $\rho = 1.0$. Toxicity converges to approximately 0.147 regardless of game structure, revealing a game-invariant property of the governance mechanism. These results establish that adaptive behavioral responses are necessary and sufficient to make externality internalization welfare-positive, and that this finding generalizes beyond the Prisoner's Dilemma payoff structure commonly used in the literature.

1. Introduction

A central challenge in governing multi-agent AI systems is the tradeoff between safety and welfare. Mechanisms that internalize externalities — forcing agents to bear the cost of ecosystem harm they cause — can reduce harmful interactions but may also suppress beneficial activity. This tension is well-studied in economic theory (Pigouvian taxation [1, 2]) but its dynamics in AI agent populations with heterogeneous capabilities and behavioral archetypes remain underexplored [14, 15].

We use the SWARM framework's soft-label formulation [18, 19], where each interaction has a probability $p = P(v = +1)$ of being beneficial rather than a binary good/bad label. Governance operates through two parameters: externality internalization ($\rho$), which controls how much agents bear the cost of ecosystem harm, and acceptance threshold adaptation, which adjusts the bar for interaction approval based on governance pressure.

This paper presents a three-study arc investigating how the welfare-toxicity tradeoff responds to (1) the level of externality internalization, (2) whether agents can learn from rejection, and (3) whether results generalize across game-theoretic structures. Each study builds on the previous, progressively answering whether the "governance sweet spot" is a robust phenomenon or an artifact of specific payoff assumptions.

2. Experimental Setup

2.1 Simulation Architecture

All experiments use the SWARM Mesa Bridge protocol [22, 23], which connects agent-based model (ABM) dynamics to the SWARM soft-label governance pipeline. At each timestep:

1. Agents update their state via archetype-specific stochastic dynamics
2. The ProxyComputer converts observable signals (task_progress, rework_count, engagement) into $\hat{v} \in [-1, +1]$, then applies a calibrated sigmoid to obtain $p \in [0, 1]$
3. The SoftPayoffEngine computes expected surplus $S = p \cdot s^+ - (1-p) \cdot s^-$ and externality $E = (1-p) \cdot h$
4. A governance decision accepts or rejects the interaction based on the acceptance threshold

2.2 Agent Population

All studies use the same 30-agent heterogeneous population:

Archetype	Count	Initial task_progress	Engagement	Learning rate
Cooperative	15	$\mathcal{N}(0.85, 0.08)$	$\mathcal{N}(0.70, 0.10)$	0.03
Selfish	10	$\mathcal{N}(0.55, 0.08)$	$\mathcal{N}(0.45, 0.10)$	0.05
Exploitative	5	$\mathcal{N}(0.25, 0.08)$	$\mathcal{N}(0.30, 0.10)$	0.02

Cooperative agents drift upward in quality; selfish agents drift slightly downward; exploitative agents drift substantially downward with high rework rates.

2.3 Governance Regimes

Regime	Threshold	Learning	Studies
Static	$\theta = 0.5$	No	1, 2
Adaptive	$\theta = 0.5 + 0.3\rho$	No	1, 2, 3
Adaptive + Learning	$\theta = 0.5 + 0.3\rho$	Yes	2, 3

Learning mechanism: when rejected, an agent improves its task_progress by $\text{lr} \times (1.0 - \text{task_progress})$, with diminishing returns as quality approaches 1.0.

2.4 Game Structures (Study 3)

Game	$s^+$	$s^-$	$h$	$p_{\text{break-even}}$ (surplus)	$p_{\text{break-even}}$ (with externality)	Character
Prisoner's Dilemma	2.0	1.0	2.0	0.33	0.60	Temptation to defect
Stag Hunt	4.0	0.5	1.0	0.11	0.27	Coordination game
Hawk-Dove	1.5	2.0	3.0	0.57	0.77	Costly conflict

The game structures follow canonical forms from evolutionary game theory [6, 7, 9]. The break-even probability $p_{\text{be}}$ is derived from the point where expected surplus minus externality equals zero: $p_{\text{be}} = (s^- + h) / (s^+ + s^- + h)$.

2.5 Sweep Parameters

Study	Swept Parameters	Seeds	Total Runs
1: Governance	$\rho \in {0.0, 0.1, \ldots, 1.0}$, regime $\in$ {static, adaptive}	5	110
2: Adaptive Agents	$\rho \in {0.0, 0.1, \ldots, 1.0}$, regime $\in$ {static, adaptive, learning}	5	165
3: Game Structures	$\rho \in {0.0, 0.2, 0.4, 0.6, 0.8, 1.0}$, regime $\in$ {adaptive, learning}, game $\in$ {PD, SH, HD}	5	180
Total			455

Each run simulates 50 timesteps with 30 agents, producing 1,500 interactions per run.

2.6 Metrics

• Toxicity: $E[1-p \mid \text{accepted}]$ — expected harm from interactions that pass governance
• Total welfare: cumulative payoff across all agents and timesteps
• Quality gap: $E[p \mid \text{accepted}] - E[p \mid \text{rejected}]$ — positive means governance selects for quality
• Acceptance rate: fraction of interactions accepted

3. Results

3.1 Study 1: Externality Internalization Is a Pure Tax Without Adaptation

Regime	$\rho$	Toxicity	Welfare	Acceptance	Quality Gap
Static	0.0	0.237 $\pm$ 0.009	1141.2 $\pm$ 24.2	0.59	+0.434
Static	0.5	0.237 $\pm$ 0.009	906.8 $\pm$ 24.6	0.59	+0.434
Static	1.0	0.237 $\pm$ 0.009	720.7 $\pm$ 26.4	0.59	+0.434
Adaptive	0.0	0.237 $\pm$ 0.009	1141.2 $\pm$ 24.2	0.59	+0.434
Adaptive	0.5	0.214 $\pm$ 0.005	906.8 $\pm$ 25.4	0.53	+0.423
Adaptive	1.0	0.157 $\pm$ 0.004	339.8 $\pm$ 46.9	0.19	+0.317

Finding 1: In the static regime, $\rho$ has zero effect on toxicity, quality gap, or acceptance rate — it only reduces welfare proportionally. This is because the payoff reduction from $\rho$ is symmetric across interaction quality levels.

Finding 2: In the adaptive regime, $\rho$ drives the acceptance threshold upward, creating a genuine screening mechanism. Toxicity drops 34% from 0.237 to 0.157 at $\rho = 1.0$, but at the cost of 70% welfare reduction and 68% acceptance rate collapse.

Finding 3: The governance sweet spot lies at $\rho \in [0.3, 0.7]$, where toxicity reduction is statistically significant ($p < 0.01$) but welfare loss remains moderate.

3.2 Study 2: Learning Agents Recover Welfare Collapse

Regime	$\rho$	Toxicity	Welfare	Acceptance	Selfish $\bar{p}$	Selfish final TP
Adaptive	0.0	0.237	1141.2	0.59	0.408	0.264
Adaptive	0.8	0.199	719.1	0.44	0.408	0.264
Adaptive	1.0	0.157	339.8	0.19	0.408	0.264
Adaptive + Learning	0.0	0.272	1271.0	0.72	0.520	0.533
Adaptive + Learning	0.8	0.193	869.4	0.52	0.606	0.685
Adaptive + Learning	1.0	0.147	807.0	0.42	0.608	0.690

Finding 4: Learning agents recover +137% welfare at $\rho = 1.0$ (807.0 vs 339.8; $d = 11.30$, $p < 0.001$). The learning regime Pareto-dominates adaptive-only at every $\rho$ value.

Finding 5: Selfish agents are the primary beneficiaries of learning, improving task_progress from 0.264 to 0.690 (+161%). Exploitative agents improve only modestly (0.135 to 0.197, +46%) due to lower learning capacity and higher rework rates.

Finding 6: The governance safe zone widens from $\rho \in [0.3, 0.7]$ (adaptive-only) to approximately $[0.0, 0.8]$ with learning agents. The concept of a "sweet spot" may be obsolete — with learning, $\rho$ is beneficial at all levels.

3.3 Study 3: Results Generalize Across Game Structures

3.3.1 Welfare at $\rho = 0$ and $\rho = 1.0$

Game	Regime	Welfare ($\rho$=0)	Welfare ($\rho$=1)	Change	Toxicity ($\rho$=1)
PD	Adaptive	1141.2	339.8	-70.2%	0.157
PD	Learning	1271.0	807.0	-36.5%	0.147
Stag Hunt	Adaptive	2596.1	876.0	-66.3%	0.157
Stag Hunt	Learning	2980.2	2033.6	-31.8%	0.147
Hawk-Dove	Adaptive	594.3	134.9	-77.3%	0.157
Hawk-Dove	Learning	588.0	348.9	-40.7%	0.147

3.3.2 Learning Benefit at $\rho = 1.0$

Game	Welfare Recovery	Cohen's $d$	$p$-value
Prisoner's Dilemma	+137.5%	11.30	$< 0.001$
Stag Hunt	+132.2%	11.63	$< 0.001$
Hawk-Dove	+158.7%	9.88	$< 0.001$

Finding 7: Learning agents Pareto-dominate across all three game structures. The welfare recovery percentage ranges from 132% (Stag Hunt) to 159% (Hawk-Dove), with all effects achieving massive effect sizes ($d > 9$).

Finding 8: Hawk-Dove shows the strongest percentage recovery because its high externality cost ($h = 3.0$) creates the largest gap between adaptive-only collapse and learning-enabled recovery. The absolute welfare at $\rho = 1.0$ with learning (348.9) exceeds the adaptive-only welfare at $\rho = 0.6$ (296.2).

Finding 9: Toxicity at $\rho = 1.0$ converges to 0.157 (adaptive) and 0.147 (learning) regardless of game type. Game structure affects welfare magnitude but not the effectiveness of toxicity reduction. This suggests the governance mechanism operates on a dimension orthogonal to payoff structure.

3.3.3 Normalized Welfare Decay

When welfare is normalized to each game's $\rho = 0$ baseline, the decay curves nearly overlap across game types (Figure 12). Under the adaptive-only regime, all three games lose approximately 70% of welfare at $\rho = 1.0$. With learning, the loss is reduced to approximately 32--41%. This game-invariant decay rate is a central finding: it implies that the governance tradeoff is structurally determined by the agent population dynamics, not the payoff matrix.

3.4 Cross-Study Validation

Study 2 and Study 3 share the Prisoner's Dilemma condition with identical parameters. The results are numerically identical across both studies (welfare 339.8 adaptive, 807.0 learning at $\rho = 1.0$), confirming reproducibility and validating the experimental pipeline.

3.5 Figures

Figure 8: Total welfare as a function of externality internalization ($\rho$) for three game types. Orange (Adaptive + Learning) consistently dominates blue (Adaptive) with the gap widening at high $\rho$.

Figure 9: Toxicity as a function of $\rho$. Both regimes follow nearly identical toxicity reduction curves. The dashed line marks $\tau = 0.15$.

Figure 10: Welfare recovery percentage (learning over adaptive-only) by game type and $\rho$. The benefit is modest at low $\rho$ (~10--15%) but explodes at $\rho = 1.0$ (130--160%).

Figure 11: Welfare-toxicity Pareto frontier. The learning regime (orange) strictly dominates the adaptive regime (blue) at every $\rho$ level. Labels show $\rho$ values. Hawk-Dove exhibits a welfare reversal at high $\rho$ where learning welfare exceeds adaptive welfare at $\rho = 0.6$.

Figure 12: Welfare as percentage of $\rho = 0$ baseline. Decay curves overlap across game types, demonstrating game-invariant governance dynamics. The 80% collapse line is shown for reference.

4. Discussion

4.1 The Tax-to-Mechanism Transition

Our results reveal a sharp qualitative transition in the role of externality internalization. Without adaptive acceptance thresholds (static regime), $\rho$ is literally a Pigouvian tax [1, 2] — it reduces payoffs uniformly without affecting selection quality. This is because the governance pipeline's acceptance decision is decoupled from the payoff structure. The adaptive threshold creates the coupling that transforms a tax into a mechanism [3, 4, 5], linking $\rho$ to actual behavioral consequences (rejection of low-quality interactions).

4.2 Learning as a Pareto Improvement

The introduction of learning agents [10, 11] does not merely shift the welfare-toxicity tradeoff — it expands the Pareto frontier. At every $\rho$ level, the learning regime achieves both higher welfare and comparable or lower toxicity. This occurs because learning converts rejection from a pure loss (excluded agents contribute nothing) into an investment (excluded agents improve and re-enter). The selfish archetype is the key swing group: their moderate learning rate (0.05) allows substantial improvement, and their population share (33%) means their behavioral shift significantly impacts aggregate outcomes.

4.3 Game-Invariance of the Governance Mechanism

Perhaps the most striking finding is the near-perfect convergence of toxicity at $\rho = 1.0$ across game types. Despite radically different payoff structures — from the low-threshold, high-reward Stag Hunt [9] ($p_{\text{be}} = 0.27$) to the high-threshold, high-cost Hawk-Dove [6, 7] ($p_{\text{be}} = 0.77$) — the governance mechanism achieves the same toxicity reduction. Combined with the overlapping normalized decay curves, this suggests that the governance tradeoff is a property of the agent population dynamics [24] (archetype distribution, learning rates, stochastic drift) rather than the interaction payoff structure. The payoff matrix determines the welfare scale but not the governance shape.

4.4 Implications for AI Governance Design

These findings support a design principle for multi-agent AI governance [12, 14, 16, 17]: governance mechanisms should be paired with adaptation incentives. A pure externality tax will always reduce welfare; pairing it with (1) adaptive acceptance criteria and (2) feedback loops that allow agents to improve creates a qualitatively different outcome. The game-invariance result is particularly encouraging: it suggests that governance designers need not know the exact payoff structure of the interactions they are governing — the mechanism generalizes.

5. Conclusion

Across 455 simulation runs spanning three studies, we establish that externality internalization ($\rho$) combined with adaptive acceptance thresholds and agent learning produces consistent welfare-toxicity improvements that generalize across Prisoner's Dilemma, Stag Hunt, and Hawk-Dove game structures. The key mechanism is the conversion of rejection from exclusion to improvement: learning agents that increase quality in response to governance feedback recover 132--159% of the welfare lost to governance pressure ($d = 9.88$--$11.63$, all $p < 0.001$), Pareto-dominating the non-learning regime at every level of externality internalization. Toxicity converges to approximately 0.147 at full internalization regardless of game type, revealing a game-invariant property of the governance mechanism. These results establish that adaptive behavioral responses are necessary and sufficient to make externality internalization welfare-positive, and that governance designers need not know the exact payoff structure of the interactions they govern.

6. Limitations

1. Synthetic agent dynamics: All agents follow prescribed stochastic dynamics rather than executing real strategies. The learning mechanism is a simple gradient rather than a strategic response, and agents do not reason about the governance system.
2. Fixed population: The 30-agent population (15/10/5) is fixed across all studies. Results may not hold at different scales or compositions.
3. No adversarial learners: The current learning mechanism is honest — agents genuinely improve quality. Strategic agents might learn to game the threshold (e.g., improving observable signals while maintaining harmful behavior).
4. Single proxy pipeline: All studies use the same ProxyComputer weighting. Different proxy configurations could yield different governance tradeoffs.
5. No communication or coalition formation: Agents act independently. Coalition dynamics (collusion, coordinated threshold dancing) are not modeled.
6. Discrete game types: We test three canonical 2x2 games but not continuous payoff space interpolation or asymmetric games.

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Paper scaffold generated from SWARM run data. Run directories: 20260224-220829_mesa_governance_study, 20260226-201109_mesa_adaptive_agents_study, 20260226-211430_mesa_game_structures_study. Cross-study comparison: cross_study_mesa_comparison.