Each player has an endowment to split between a private account and a public pot — will free-riding prevail?
Game Parameters
Group size (N)4
Endowment (E)20
Multiplier (m)1.6
Payoff = (E − cᵢ) + (m · ΣC) / N
where cᵢ = your contribution, ΣC = group total
Socially optimal: contribute E (all in)
Nash equilibrium: contribute 0 (free ride)
Dilemma exists when: 1 < m < N
✓ Dilemma exists: m/N = 0.40 < 1 (defect is dominant) but m = 1.6 > 1 (group gains from contributing).
Institutional Mechanism
Baseline
Punishment
Reward
Threshold
No institution: Standard VCM. The dominant strategy is to contribute 0. Experimental finding: contributions start ~40-60% of endowment and decay toward 0 over rounds.
Punishment cost ratio0.33
Punishment impact ratio1.0
Peer punishment: After contributions are revealed, you can spend tokens to reduce low contributors' payoffs. Costs you cost per unit, reduces them by impact per unit. Fehr & Gächter (2000) found this sustains cooperation.
Reward cost ratio0.33
Peer reward: After seeing contributions, you can spend tokens to reward high contributors. Each token you spend gives them 1 token. Less effective than punishment empirically, but creates positive reciprocity.
Provision threshold (%)50
Provision point: The public good is only provided if total contributions reach the threshold. Below it, contributions are refunded. Creates a coordination game instead of a pure free-rider problem.
Each token you keep earns 1. Each token in the pot earns m/N = 0.40 per person. Since 0.40 < 1, the private return from contributing is negative — but the group earns m = 1.6 per contributed token. This is the dilemma.
Contributions Over Time
Your Contribution
Avg. Others
Group Average
Social Optimum
Cumulative Earnings
You
Avg. Others
If All Cooperated
The Free-Rider Problem Explained
Marginal Private Return
Each token you contribute returns m/N = 0.40 to you. Since this is < 1, you're better off keeping it. This is why free-riding is the Nash equilibrium.
Marginal Social Return
Each token contributed returns m = 1.6 to the group. Since this is > 1, every contribution creates a net social gain. This is why full contribution is socially optimal.
The Efficiency Gap
If all contribute E: each earns —. If all contribute 0: each earns —. Efficiency loss: —%.
Experimental Evidence
Lab experiments consistently find: ~40-60% initial contributions, decay to ~10-20% over 10 rounds, restart effects, and punishment sustains cooperation at ~80-90%.