[13a] Public Goods Contribution Game

Learning Goals

(a) See why privately optimal choices can under-provide public goods
(b) Observe dynamics of trust, norms, and reciprocity

Timeframe

35–45 minutes total:

  • (5’) Setup & instructions
  • (20’) Rounds 1–5 (4 mins each)
  • (10’) Quick plotting & debrief

Grouping & Budgets

Each player in each group (4–6 players) receives $20 tokens per round.

Payoff function:
In each round, a player chooses how much to contribute ( c_i ∈ {0,1,…,20} ) to the group account, keeping the rest ((20-c_i)) privately.

The group account is multiplied by M = 1.6, and divided equally among the number of group members.

[ \text{payoff}i = (20 - c_i) + \frac{1.6 \times \sum{j=1}^N c_j}{N} ]

Then, per-capita MR = 1.6 / N.
E.g., if N=5, MR = 0.32.

So free-riding is privately optimal, but socially inefficient.

Procedures (Rounds)

Baseline (No communication; no punishment; no subsidy)

  • Players decide contribution ( c_i ∈ {0,1,…,20} ). No talking.
  • Instructor/TAs collect numbers and compute group sum C and average contribution.
  • Announce each group’s C and average; players compute own payoff.

Communication only

  • 1 minute open chat per group (no binding promises).
  • Contribute again.
  • Record and announce C, average, payoffs.

Peer-punishments

  • After seeing contributions from Round 2, each player may assign punishment points to others ( p_{i→k} ∈ {0,1,2} ) within the group. No talking.
  • Cost to punisher: 1 point per punishment point assigned.
  • Cost to punishment recipient: 3 points per punishment point received.
  • Compute payoffs: baseline payoff – costs – punishment.
  • Announce C, total punishments used.

Matching subsidy

  • For every token contributed, the instructor matches +0.5 into the group account.
    (Effective multiplier = 1.6 + 0.5 = 2.1).
  • No talking. Decide contributions under the matching rule.
  • Repeat contribution, announce results.

Policy mix (communication + matching)

  • 1 minute open chat.
  • Contribute under matching rule.
  • Announce results.

Visualization

During the game, visualize data on the board:

  • Create a simple table by round and average contribution per group.
  • Goal: show the typical rise after communication, stabilization with punishment, and often the highest with matching.
  • Allow for noise.

Debrief Questions

  • Which institution sustained cooperation best in your group? Why?
  • Did communication produce conditional cooperation (“I’ll contribute if you do”)?
  • Was punishment used efficiently or did it backfire?
  • Compare total payoffs across rounds: which rule maximized welfare?
  • If the matching budget is limited, how would you target it?
  • How do these results relate to climate mitigation / campus recycling / open-source contributions?

Possible Variations

  • Heterogeneous endowments: Some players get 30, others 10. Equity debate possible.
  • Shock: Reduce multiplier to 1.1 in a round to model “bad times.”