The public goods game

The public goods game is an \(N\)-player generalisation of the traditional prisoner's dilemma. Like the prisoner's dilemma, each player may either cooperate or defect, and the game follows the process:

  1. Each player chooses whether to cooperate or defect
  2. Players who cooperate contribute \(\alpha\) to the group. Those who defect do not
  3. The total contribution is multiplied by some value \(r\)
  4. This multiplied amount is split between all players evenly, regardless of whether or not they contributed.

The payoff of each player is given by:

\[ f_i(a) = \frac{r\sum_{j=1}^N \alpha_j}{N} - \alpha_i \]

Where \(\alpha_i\) is the amount contributed by player \(i\). It takes the value 0 if player \(i\) defects, and the value of their contribution if they cooperate. The contribution of different players may be a heterogeneous attribute of the population.

See Hauert et al. (2002) in the bibliography.