We first describe the general procedure, and then provide details about our treatments.
In each session, 16 participants play 4 repeated public goods games in groups of 4 players. Each game consists of 8 rounds. In each round, participants choose how to allocate 10 tokens between a private account and a group account. After each game, groups are reformed using a stranger matching procedure. Participants are only identified by a randomly generated ID number. It is common knowledge since the beginning that only one of the 4 games will be randomly selected for payments, and that each player will be paid the sum of earnings made in the 8 rounds that constitute that game. In all treatments, the instructions specify which are possible values that the MPCR can take. The minimum possible value of the MPCR is 0.05 and the maximum is 1.25, with increments of 0.1. There are therefore 13 possible values that the MPCR can take. In all treatments, subjects are told that in 3 out of 4 games the true MPCR is constant within each game (e.g. the MPCR does not vary between rounds); instead, in one of the 4 games the true MPCR is randomly drawn every round (with replacement) from the 13 possible values. In all treatments, the 3 games with constant MPCR have always the following (predetermined) MPCR values: 0.25, 0.55, and 0.95. We have two sessions per treatment, and we (partially) vary the order in which games are played : in one session the order of games is: 0.25, 0.55, 0.95, VARIABLE; in the other the order is 0.95, 0.55, 0.25, VARIABLE. Before the beginning of each game, participants are informed about whether the game has a constant or variable MPCR. To control for risk and ambiguity preferences, at the end of the experiment all participants play an incentivized Eckel-Grossman risk task (Eckel and Grossman 2002), and an ambiguity task. This basic structure is common to all treatments.
We have a total of four treatments in our experiment plus a baseline. We have thus a total of 160 subjects, equally balanced across treatments. The baseline treatment Base-VCM is a standard public goods game without Knightian uncertainty.
We have two private signal treatments in which participants only observe their own signal. In treatment Private Thin each participant receives a private signal known to be drawn from the interval: true MPCR +/- 0.1. So for instance if a participant receives a private signal of 0.55, he knows that the true MPCR can either be 0.45, 0.55, or 0.65. He also knows that if the true MPCR is, for instance, 0.65, another player might have received a signal of 0.55, 0.65, or 0.75. Differently, in treatment Private Thick participants receive a private signal known to be drawn from the interval: true MPCR +/- 0.2. So for instance if a participant receives a private signal of 0.55, he knows that the true MPCR can either be 0.35, 0.45, 0.55, 0.65, or 0.75.
We have two public signals treatments, Public Thin and Public Thick, that have the same parameters of the private conditions, but differ in the fact that participants also observe the signals of other group members.
The original experiment was conducted at the ExCEN experimental laboratory at Georgia State University, and was programmed using O-Tree (Chen et al. 2016). Participants received a show-up fee of $10.
Three independent teams will replicate the study. Here is the list of scholars who will independently replicate the study and will coauthor the second study that will be sent to an refereed journal for publications:
1. Phillip Grossman - Monash University.
2. Daniel Houser - George Mason University.
3. Marie Claire Villeval - CNRS and University of Lyon.