Public Goods (Signaling): with Reward/Punishment Option

Game Description

Each student is part of a group (an orchestra). Each week, each student chooses how many of her 20 hours to contribute to the public good (working with her Ensemble section as opposed to working on her Solo). This environment highlights the distinction between individual incentives and collective interests: a student earns 3 prestige points for each hour dedicated to Solo, and every member of the group earns 1 prestige point for an hour allocated to Ensemble.

This is one of three MobLab games considering the voluntary private provision of a public good. 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 students have an incentive to free ride. In both this game and Linear Public Goods, equilibrium contributions are zero.

This game differs from Linear Public Goods in two respects. First, by choosing Transparency, you can have players learn each group member’s contributions. Second, you can choose to allow each player to Punish or Reward other group members.

Learning Objective 1: 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.

Learning Objective 2: Effects of Punishments/Rewards

Some individuals choose to punish low contributions or reward high contributions even if not part of a subgame-perfect Nash equilibrium. In order to avoid punishment or accrue reward, some individuals may increase contributions even if the personal monetary cost is greater than the monetary benefit. As a result, the existence of reward and punishment opportunities may increase voluntary contributions to public goods.

Brief Instructions

To show the effects of allowing rewards or punishment, first run a multi-round baseline game (with neither rewards nor punishments). If you choose Transparency, you can have players learn each group member’s contributions. Otherwise, a player learns only the sum of Ensemble contributions.

Once the baseline game is finished, choose Replay. (Using Replay makes it easier to compare outcomes between games.) Choosing Random shuffles group composition between games. In the resulting popup, select Punishment or Reward (or both), and also select Transparency. (If you do not select Transparency, punishments and rewards will be less effective as a player will not know the contributions chosen by individual group members.)

With punishment (reward), a player spends an hour of her practice time hindering (helping) another player, decreasing (increasing) the target’s payoff by 3 points. Importantly, each hour a player spends punishing or rewarding fellow group members decreases time available to divide between Solo and Ensemble, and is thus costly to the punisher (rewarder). Also, while Transparency reveals each person’s choices at the end of a round, a player will not know this round’s choices by group members when choosing this round’s rewards or punishments.

Important: Due to the amount of information available to players, the maximal Group Size is 6. You will want to set a Group Size of at least 4 to have public-good contributions (i.e., choosing Ensemble) increase total surplus.

Key Treatment Variations

If you choose Show Identity, contributions (and reward and punishment decision, if applicable) are linked to the name a student used when registering for MobLab. This tends to increase contributions relative to Transparency, where other players are known by generic player numbers.

Other Parameters

  1. With Default Contribution set to 0 (the default), a player’s slider starts at 0 hours contributed to the public good, which he can increase. Increasing a player’s default contribution will likely result in increased early-round contributions.
  2. With Round Duration set to -1 (the default), a group proceeds to the next round only when all group members have submitted a choice. Setting an actual Round Duration sets a maximal round duration in the event that not all players have submitted a choice. Here are your options for what happens when a round times out:
    1. By default, if a round times out before a student has made a choice, he is considered to have chosen no hours of either Ensemble or Solo. His payoff for the round is zero. In calculating the payoffs of group members, he contributes no Ensemble hours.
    2. Alternatively, if you choose Proxy Play (available under Advanced), a robot will make a choice on behalf of a student who does not make a choice before round’s end.


Our across-game results allow you to compare public-good contributions across different conditions.

Note: After playing a first game, you must start subsequent games using Replay in order to display multiple games in the same graph.

Figure 1: Game Parameters

To access across-game results, after the last game is complete, choose Results for this last game. The resulting chart (see Figure 1) shows contributions across rounds (horizontal axis) for each game. In particular, the vertical axis shows ensemble hours as a fraction of total hours (20 × number of students). Click the checkbox next to the game name in the legend to hide a particular series. Mousing over a data point will show the exact percentage.

Robot Play

In the first round robots contribute a random number (between 0 and the Endowment) to the orchestra. 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.

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