The Entry Fee That Keeps Adversaries Out of the Fair Division Pool¶
A parameter sweep reveals a sharp screening threshold: below fee=6.0 every agent joins; above it, adversarials self-select out
Our contract screening mechanism showed that costly contracts can separate honest agents from adversaries. But the original cake-splitting experiment had a problem: with an entry fee of 2.0, every agent --- including the adversarial one and both deceptive agents --- joined the fair division pool. Infiltration rate = 1.0. The fee wasn't high enough to screen anyone.
So we swept it.
The experiment¶
We took the cake_splitting.yaml scenario (10 agents: 4 honest, 3 opportunistic, 2 deceptive, 1 adversarial) and swept the fair division entry fee over 8 values: 0.5, 1.0, 2.0, 4.0, 6.0, 8.0, 10.0, 15.0. Three seeds per fee level, 24 total runs. Everything else held constant: 20 epochs, 10 steps per epoch, redistribution rate 0.3, fairness bonus 0.08.
The question: at what fee do adversarial agents decide the fair division pool isn't worth entering?
The result: a phase transition at fee=6.0¶
The transition is binary. At fee <= 4.0, infiltration rate = 1.0 across all seeds. At fee >= 6.0, infiltration rate = 0.0 across all seeds. There's no gradual decline --- the mechanism flips from "everyone joins" to "adversarials stay out" in a single step.
This makes sense. Each agent runs a utility calculation: preference * quality_belief * resources - cost - switching_penalty. Adversarial agents have low fair-division preference (0.1) and low resources relative to honest agents. At fee=4.0 the expected benefit still exceeds the cost. At fee=6.0 it doesn't. The crossover is sharp because the utility function is linear in fee.
What changes when adversarials leave¶
When the infiltration rate drops to zero, total welfare ticks up from ~366.8 to ~368.3. That's a modest 0.4% improvement --- but it's consistent across all three seeds and all fee levels above the threshold.
Toxicity shows a similar small improvement: 0.335 to 0.337 average. The effect is small because the adversarial agent is only 1 of 10 agents, and the scenario's governance levers (staking, circuit breaker, transaction tax) already constrain its damage.
Agent payoffs are stable¶
The payoff ordering is consistent across all fee levels: honest (~55) > opportunistic (~41) > deceptive (~8) > adversarial (~5). Entry fee doesn't meaningfully change anyone's payoff --- it changes where agents participate, not how much they earn.
This is actually the point. The entry fee is a screening mechanism, not a punishment mechanism. It doesn't need to reduce adversarial payoffs to work. It just needs to make the fair division pool unattractive to agents who would degrade its quality.
The mechanism design lesson¶
The screening threshold depends on the interaction between three parameters:
- Entry fee (what the agent pays)
- Type-specific preference (how much the agent values fair division)
- Agent resources (what the agent can afford)
For this scenario configuration, fee=6.0 is the minimum where adversarial expected utility goes negative. But this number isn't universal --- it depends on the preference weights, the fairness bonus, the redistribution rate, and the initial resource endowment.
The general principle: set the entry fee above the adversarial indifference point but below the honest indifference point. The gap between these two points is your mechanism's slack. A wider gap means more robustness to parameter uncertainty.
In our scenario: - Honest fair preference: 0.9 - Adversarial fair preference: 0.1 - Gap: 9x
That 9:1 preference ratio gives the mechanism plenty of room. The fee can be anywhere from 6.0 to well above 15.0 without losing honest agents.
Why the transition is sharp, not gradual¶
In many governance mechanisms, increasing stringency produces gradual effects --- more audits catch slightly more cheaters, higher taxes slightly reduce exploitation. The entry fee is different because it's a binary decision: join or don't join. Each agent either clears the utility threshold or doesn't.
With only 3 adversarial-class agents (1 adversarial, 2 deceptive), the transition appears as a step function. In a larger population with heterogeneous preferences, you'd expect a smoother S-curve as different agents hit their indifference points at different fee levels.
Reproduce it¶
The sweep produces a CSV in runs/<timestamp>_cake_entry_fee_sweep/sweep.csv with 24 rows and a summary table printed to stdout.
What's next¶
- Finer grid around the threshold: Sweep [4.0, 4.5, 5.0, 5.5, 6.0] to pin down the exact crossover
- Adaptive adversaries: What if the adversarial agent learns to increase its fair-division preference over time?
- Joint sweep: Sweep entry fee and redistribution rate simultaneously to map the 2D screening surface
- Larger populations: 50+ agents with continuous preference distributions to test whether the S-curve hypothesis holds
Disclaimer: This post uses financial market concepts as analogies for AI safety research. Nothing here constitutes financial advice, investment recommendations, or endorsement of any trading strategy.