Linear Public Goods

Game Description

Students choose how much to contribute to a public good (a water purification project) where the amount of public good provided increases linearly with total contributions. This is a great environment to study the distinction between individual incentives and collective interests: the individual receives less than $1 in benefit from contributing $1, but the group's benefit is greater than $1.

Note: This is one of three MobLab public goods games. In this game and Public Goods (Signaling), the private returns from contributing are always less than the private returns from the alternative, but the latter game has the option of allowing players to punish or reward group members. In Threshold Public Goods, where students choose whether to contribute to a public good project that is implemented only if contributions exceed the project’s cost, there are equilibria in which contributions are sufficient to pay for the public good, but each prefers equilibria where others contribute more (or all). Thus, while the Threshold game focuses on the coordination problem inherent in some voluntary contribution environments, the Linear games highlight the distinction between private and societal benefits of a contribution.

Learning Objective 1: Private Versus Societal Benefits

Because benefits are non-rival, private benefits of a contribution to a public good will be less than societal benefits (equal to the private benefit of all who benefit).

Learning Objective 2: Voluntary Contributions

As an individual bases her provision of a public good on her private benefit (under standard assumptions), relying on voluntary contributions will result in an inefficiently low level of provision.

Brief Instructions

The Rate of Return (%) is each group member’s benefit from a $1 contribution to the public good. Contribution increases surplus when Rate of Return (%) × Group Size is greater than 1, in which case the efficient outcome has each player contributing her entire endowment.

With the default parameters (Rate of Return (%)=50%; Group Size=4), contribution is efficient, but the likely outcome is a moderate level of initial contributions (on the order of 50% of group endowment, on average) which decays with each passing round.

Key Treatment Variations

  1. Allowing Chat will generally increase contributions as it may help foster a norm of giving.
  2. Increasing the Rate of Return will generally increase contributions.
  3. Perhaps counterintuitively, it is possible that increasing Group Size (holding constant rate of return) may well increase contributions, potentially because of the increase in societal benefits per unit of individual contribution.


Figure 1: Switching Between Rounds

In the results, you will see evidence of free riding. In particular, while you may well see reasonably high round-one contributions, contributions will decay relatively rapidly across rounds. We start by looking at the details of a particular round, choosing that round from the Go To drop down (Figure 1).

Figure 2: Game Parameters
Figure 3: Group Outcomes in a Particular Round

The top table (Figure 2) displays the parameters (e.g., group size, rate of return) chosen for the game. The next table (Figure 3) shows contributions and average payoffs for each group for the chosen round, as well as for the equilibrium and efficient benchmarks. It will show that higher contributing groups will have higher average payoffs. Click the column header to sort by that column.

Figure 4: Distribution of Contributions

The last graph (Figure 4) shows the distribution of contributions in the chosen round. While early-round contributions will be widely distributed, by later rounds most players will choose little or no contributions.

Figure 5: Contributions Across Rounds

We now switch to multi-period summaries, choosing Multi-Period Summary from the Go To drop down (Figure 1). The top table (Figure 2) displays the parameters constant across rounds (e.g., group size, rate of return), while the two charts (Figure 5) summarize contributions across rounds. On the left, the box-and-whiskers chart summarizes contributions at the individual level, showing for each round the inter-quartile range of contributions (the box) as well as the minimum and maximum contribution (the whiskers). In addition, the mean is indicated with a red marker and the median with a white line within the box. On the right, the chart summarizes contributions by round at the group level. On the vertical axis, we display group contributions as a percentage of group endowments, and plot for each round the highest, lowest and median contributing group.

Robot Play

In the first round robots contribute a random number (between 0 and the Endowment) to the water sanitation project. In each subsequent round the robot is a conditional cooperator. In other words, the robot makes a contribution equal to the average of other's contributions in the previous round.

tiled icons