Conflux — About & FAQ

Conflux is an interactive lab for public-goods dynamics. It lets you simulate how incentives (tax, reward, punishment), network topology, and behavioral rules shape cooperation and welfare over time.

Quick Tour

  • Home: play with parameters and watch curves evolve.
  • Experiments: run grid sweeps and visualize outcomes with a heatmap.
  • Compare Topologies: overlay well-mixed vs small-world for the same settings.

Model Overview

In each round, agents receive an endowment w and choose a contribution ci∈[0,w]. The sum of contributions is multiplied by a marginal per-capita return (a) and redistributed. Policies add incentives: taxes for under-contributing, rewards for generous contributors, and punishment for defectors. Noise captures execution jitter and imperfect observation.

Parameters & Implications

Core

nPopulation size. Larger n increases payoff dilution; cooperation is harder without mechanisms.
wPer-round endowment. Upper bound on each contribution.
a (MPCR)Marginal per-capita return. If a<1, pure egoists defect unless incentives counterbalance.
TNumber of rounds. Longer horizons allow beliefs to stabilize.

Noise

σ_execExecution noise: agents miss intended contribution (trembling-hand). Can accidentally nudge cooperation.
σ_obsObservation noise: misperceive others’ contributions. Increases misclassification under punishment.

Mechanisms

Tax (on low c)Activated when c<τ·w, levies rate·(w−c). Discourages free-riding.
τ (threshold)Low contributions below τ are penalized. Higher τ is harsher.
Reward (for high c)Activated when c≥ρ·w, grants rate·c. Encourages generosity.
ρ (threshold)Higher ρ targets only top contributors; lower ρ spreads rewards widely.
PunishmentExpected fine on under-contributors. Effective but may reduce welfare if overused under noise.
finePenalty magnitude on defectors.
punishers shareShare of potential punishers in the population/neighborhood.

Topology

well-mixedEveryone interacts with everyone. One global public good.
small-worldWatts–Strogatz neighbors + rewiring. Local public goods; clusters can sustain cooperation.
kInitial ring degree (even). Higher k broadens neighborhoods.
pRewire probability. Larger p reduces path length; may mix behavior faster.

Agent Types

  • Egoist: best-response to current beliefs, accounting for mechanisms and risks.
  • Conditional Cooperator: tends toward the believed average contribution.
  • Punitive Cooperator: like CC, but benefits from punishing defectors (modeled as expected risk).
  • Altruist: contributes high fraction regardless of beliefs (e.g., 0.8·w).

Common Patterns & Tips

  • When a<1, incentives are needed for egoists to cooperate.
  • Under high σ_obs, generous punishment backfires due to misclassification.
  • Small-world topology can preserve cooperative clusters even if global cooperation is low.
  • Rewards often lift average welfare, taxes/punishment can lift cooperation but may reduce welfare if too harsh.

FAQ

Is the punishment stage explicit?

For speed and clarity, Conflux uses an expected-penalty heuristic based on punisher share and thresholds. A full second-stage model is on the roadmap.

How are beliefs updated?

Agents track a scalar belief about average contributions and update with an adaptive learning rate that increases with prediction error.

Why two topologies?

Well-mixed approximates mean-field interaction; small-world captures local clustering and short paths—good proxies for many real networks.

Can I export results?

Yes—use CSV export on the Experiments page. For full reproducibility, save the config alongside results.