Experimental Design
The experiment is conducted in sessions with 13 participants. Prior to the start of the game, we randomly allocate one subject in each session to the role of the authority who always participates in CR and 12 subjects to the role of players. Their roles remain unchanged throughout the experiments.
In each session, we divide the repeated game of 20 periods into two parts. The identification numbers of the players are randomly assigned between the periods. First, we implement a game with three phases, each consisting of five periods. At the beginning of the first phase, 12 players are randomly and anonymously assigned to three different institutions (NR or DR or CR). Each institution consists of four players who remain constant over five periods. Players in each institution participate in another institution at the beginning of the second and third phases. Our matching mechanism, following a within-group design, ensures that each player experiences three different institutions in a random order. That is, in each session, (i) four players go through NR, then DR, and finally CR; (ii) the other four players go through DR, CR and NR, in that order; and (iii) the last four players go through CR, then NR, and finally DR. In the second part, we implement a game of five periods. Based on previous information on the average contribution and welfare of each institution in the previous 15 periods, all players are asked to choose one institution at the beginning of this part and remain there thereafter.
Each period consists of two stages: contributions and rewards . In the contribution stage, each player is endowed with 20 tokens and asked to contribute some of these tokens to the public good. Each token contributing to the public good is multiplied by 1.6 and the resulting amount is shared equally among the players in the respective institution. This payoff function follows Nicklisch et al. (2016), maintaining a constant marginal social return from the public good for different population sizes . The remainder of the endowment benefits the player using the same tokens. The player is then asked to conjecture the average amount contributed by other players in the same institution. The more accurate the players’ conjectures, the higher the payoff they could obtain from their decisions . To avoid hedging, players are paid for either a belief elicitation task or contribution decision (with the same probability). That is, on average, players are paid for the belief elicitation task in 10 periods and for contribution decisions in another 10 periods. In contrast to the players, the authority is called upon to do nothing at this stage and earn the average profit of the players in CR for this stage . That is, players in CR contribute more, and the authority earns more.
In the reward stage, all players and authorities receive signals from players in their institution. A certain probability exists that the signals are consistent with the true contributions. Using a between-subjects design, we employ three information treatments: perfect-information, low-noise and high-noise. In the perfect-information treatment, the probability is 100%. For the low-noise treatment, the probability shifts to 90%. In the high-noise treatment, the probability decreases significantly to 50%. That is, all the signals are correct in perfect-information treatment, whereas only 90% and 50% of the signals are correct in the other two information treatments. False signals are randomly drawn from the contribution choice set, excluding the real contribution choices. Players do not receive information about signals for their contributions; that is, they do not know whether other subjects are correctly informed about their exact contribution.
In addition, all players receive an extra endowment of three points. In NR, players are not allowed to be rewarded. In DR, all players simultaneously decide on the rewards for other players in the same institution. In CR, reward decisions are delegated to the authority. The authority decides on the reward to players, and the remaining points are returned to corresponding players in CR. Each point assigned to a player results in the addition of three tokens to the rewarded player’s payoff. The remaining points of each player are exchanged for tokens in a ratio of 1:1. At the end of each period, the players learn the total amount of reward received.