Experiment 07 Public Goods
Who Pays for the Shared Benefit?
Keep your tokens or fund a project everyone can use. See how matching, visibility, and repeated play change the incentives.
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Start with “Work It Out, Step by Step” below. The optional expert section explains its symbols as you go. For more examples, use the plain-language math guide.
1. Make a Prediction
A Project Everyone Benefits From
Each player receives 10 new tokens each round. Tokens you keep earn one point each. Contributions go into a shared project, grow by the chosen multiplier, and return in equal shares to everyone, including players who contributed nothing. A public good is a benefit people can share without using up someone else’s share, such as a useful public information service. This token game is a simplified model of funding one.
2. Make Your Choice
3. Reveal the Incentives
Your Earnings and the Group’s Earnings
Free riding means receiving a shared benefit while letting others pay for it. In the starting game, contributing one more token increases the group’s total but reduces the contributor’s own points. The table records up to 12 rounds. You can change your contribution between rounds without changing the rules.
| Round | You gave | Each other player gave | Your points | Group points |
|---|
4. Change One Assumption
Who Can See, Match, or Respond?
The multiplier is the number you multiply the shared pool by. A multiplier of 2 doubles it. Matching means an outside sponsor adds tokens before the project grows. A 100% match adds one token for each token players give. The sponsor is outside the displayed group, so its cost is not included in group earnings.
With punishment on and contributions visible, every player pays 1 point to fine each lower contributor 2 points. This applies to you too. Both costs and fines leave the group; they are not transferred to another player. Points may become negative, meaning a loss. Hidden contributions prevent this rule and copying from operating.
Other players follow the exact response rule shown here. They do not learn, plan ahead, or represent real people. Matching has no budget limit in this model. Changing a rule restarts the history.
Work It Out, Step by Step
Use four players, a multiplier of 2, no matching, and no punishment. Suppose everybody gives 5 tokens.
- The four contributions add to 20. The project doubles that to 40 points.
- Divide 40 among four people. Each gets 10 project points.
- You kept 5 tokens, so you earn 5 plus 10, or 15 points. Together, the group earns 60.
- If you give 6 instead, you keep only 4. The project receives 21 tokens and returns 42 points. Your equal share is 10.5.
- You now earn 14.5 points. Your extra contribution cost you half a point, even though the group now earns 61.
In words: start with 10, subtract the 6 you gave, then add one fourth of the project’s 42 points. An extra token’s effect is called its marginal return; “marginal” here means the change caused by one more.
For experts: formal model and assumptions
How to Read the Symbols
- \(n\), \(c_i\), and \(C\)
- \(n\) counts players. \(c_i\) is player \(i\)’s contribution; the little \(i\) is a player label. \(C\) is all contributions added together.
- \(m\), \(s\), and \(u_i\)
- \(m\) is the multiplier. \(s\) is the sponsor’s matching percentage divided by 100; a 50% match means \(s=0.5\). \(u_i\) means player \(i\)’s points before punishment. Adjacent letters and parentheses mean multiply.
In words: keep the unspent tokens and add one equal share of the multiplied, matched pool. The fraction bar means division. Before punishment, the change in your points from one extra contributed token is:
The group gains \(m(1+s)-1\) points from that extra token. Individual and group interests differ when the group’s gain is positive but the individual’s gain is negative. The sponsor’s cost is excluded. Punishment subtracts 1 per fine you issue and 2 per fine you receive. These scripted responses do not solve a repeated-game equilibrium, which would require checking that each player’s whole plan is best given everyone else’s plan.
See the math reading guide for fractions and subscripts, the small labels below letters.
5. Transfer the Lesson
Who Maintains the Shared Documentation?
A team benefits from a shared guide, but writing it takes time away from each person’s own work. Would matching time, public credit, or repeated collaboration change the choice? Who would pay the cost of each rule, and could punishment destroy more value than it creates?
Concept reference: MIT’s lecture on collective action and public goods. This playground’s token amounts and response rules are teaching choices.
A Model Is a Place to Start
These small models make the incentives visible. Their results follow from their stated rules; they are not forecasts of how every person or organization behaves. A simulated strategy is a rule, not a personality.
Scenario links save the controls and random seed. To reproduce an interactive run, make the same choices in the same order. Changing a setting restarts the experiment.