## 3 Materials and Methods
### The Conditions and the Game  
In order to verify our hypotheses, we developed four different conditions that concerned the presence or the absence of a reputational system (see Table 1).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Experimental Design**} \\ \hline \multirow{4}{*}{} & \multicolumn{3}{c}{**Reception Phase**} \\ \cline{3-4}  & & **Reputation ON** & **Reputation OFF** \\ \hline \multirow{2}{*}{**Donation Phase**} & Reputation ON & \(111\) & \(111\) \\  & Reputation OFF & \(111\) & \(111\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental Design. Number of subjects for each condition.  
Like the original ultimatum game, our game included two phases: donation and reception. Furthermore, the order of the phases was constant; namely, the players played as donors in the first phase and as receivers in the second. Although the participants knew that they were interacting with other players, in reality, the subjects interacted only with our system, which was programmed in order to record the proposals made during the donation phase and to generate offers using an uniform distribution (ranging from 0 to 10 euros) in the reception phase. The system also recorded the players' decisions when they acted as Receivers, and generated a random reputation ranking when necessary for the succession of the different experimental conditions. The probability distribution of reputation was uniform as well. We specify that, in the Reputation ON conditions, the opponent's reputation was displayed from the first turn, since participants were instructed to believe that reputation was achieved by their counterparts during previous sessions acting as Donors, while the player was never characterized by a reputation score.  
In the donation phase, participants had to decide how much of their stack (from 0 to 10 euros) they wanted to offer to their counterparts 15 times. The Donors also knew that the Receivers' decision would determine their gain. Indeed, if the Receivers accepted their offers, the resources were split among them according to the Donors' will, while nobody got anything if the Receiver refused the deal. We specified to the subjects that, in our game, the exchanges were asynchronous and delayed in time. In the reception phase, players displayed their interactors as anonymous (as they were themselves), so players could not know if they had interacted with them or not before. In the sessions in which the reputation system was present, Donors could see the reputation (expressed as colored circles and ranging from +5 to \(-\)5) acquired by their counterparts. In the reception phase, the players had to evaluate the offers 15 times. Their gain in this phase followed the same rule of the previous one. Like in the donation phase, two reputational conditions were present, so reputation could or could not be visible. After each decision (i.e., accept or refuse), Receivers had to decide about the Donors' behavior by rating them with a plus or a minus. This action was requested to the players to increase reputation credibility. Nonetheless, although the players were instructed to believe that reputation was built up during previous sessions, reputation did not really evolve or change since it was randomly extracted from a uniform distribution, to have approximately the same number of observations for each reputation level.