Volunteer's Dilemma Game

In the laboratory, volunteer rates were lower in larger groups, as predicted, in groups of 2 to 12, but outcomes with no volunteer became rarer as groups grew, against the prediction; a version of the equilibrium with random noise explains the difference (Goeree, Holt and Smith, 2017). In a game played once by groups of 3 to about 100, people paid more often than the equilibrium in most groups, the rate did not fall steadily with size, and a cost of 80% of the benefit lowered paying only in groups of 3 (Kopányi-Peuker, 2019).

Here the participant plays 32 rounds, each in a new group of 2, 3, 6 or 12 members, four of the five sizes Goeree and colleagues used. Each size comes once in every four rounds, in an order drawn from the session's seed. When at least one member pays, every member gets 100 points, and each member who pays loses 20 (a setting, from 5 to 95). The other members are simulated: each pays with the symmetric equilibrium chance for the round's size, 80%, 55%, 28% and 14% in groups of 2, 3, 6 and 12, from numbers drawn before the session, so nothing the participant does changes them. At these chances at least one other member pays in 80% of rounds in every group size, so paying and not paying are worth the same on average whatever the size, and a change with group size comes from the participant, not from the points. The screens say pay or do not pay, never volunteer. The standard instructions say the other members are computer programs that follow set rules; a neutral wording leaves that line out, and the last screen then says so. Studies usually explain the purpose afterwards. One check question with feedback comes first, there is no time limit, and after each choice the participant sees how many of the other members paid and the points for the round. The study decides what the points are worth.

The main score is the share of rounds in which the participant paid, the volunteer rate. It is also reported for each group size, and the group size slope gives the change in that share each time the group doubles, from a straight line fitted to every round; below 0 means paying less often in larger groups, the direction of the equilibrium and of the bystander effect. The share of rounds in which the group got the 100 points and the points won are reported too. Paying can reflect kindness, doubt that anyone else will pay, a wish to make sure of the points or a guess about a program, so the scores describe choices in a game played for points, never a person's helpfulness, and they do not diagnose. People who know the members are programs may pay differently from people in a group of people, so compare people who saw the same instructions.