Reputation drives cooperative behaviour and network formation in human groups

Abstract

Cooperativeness is a defining feature of human nature. Theoreticians have suggested several mechanisms to explain this ubiquitous phenomenon, including reciprocity, reputation, and punishment, but the problem is still unsolved. Here we show, through experiments conducted with groups of people playing an iterated Prisoner's Dilemma on a dynamic network, that it is reputation what really fosters cooperation. While this mechanism has already been observed in unstructured populations, we find that it acts equally when interactions are given by a network that players can reconfigure dynamically. Furthermore, our observations reveal that memory also drives the network formation process, and cooperators assort more, with longer link lifetimes, the longer the past actions record. Our analysis demonstrates, for the first time, that reputation can be very well quantified as a weighted mean of the fractions of past cooperative acts and the last action performed. This finding has potential applications in collaborative systems and e-commerce.

Figure 1. The level of cooperation is significantly higher when the past actions record of players to whom to connect is available.

(A): Level of cooperation (fraction of cooperative actions) per round, averaged over all experiments for the same treatment (memory m = 0, 1, 3, 5). (B): Average connectivity (ratio of actual links to potential links) per round, averaged over all experiments for the same treatment. Equivalently, fraction of links of the actual graph with respect to the complete graph. In both, (A) and (B), error bars represent plus/minus one standard deviation of a binomial distribution over the size of the treatment concerned and the number of analyzed rounds. (C): Representation of the connectivity graphs resulting from experiments with 25 participants for all four treatments. Node areas are proportional to their degrees at that round. Node colors represent the cooperation level (fraction of cooperative actions) up to that round. (We will show below that level of cooperation is an important part of reputation.) Link widths are proportional to their persistence (number of rounds they have been present). Although represented differently for the sake of consistency, the initial condition is, in all four cases, topologically equivalent to a ring where each node is linked to its first and second neighbours.

Figure 2. Reputation is a weighted combination of average cooperation and last action, and it strongly conditions linking.

If the fraction of link proposals accepted from a proponent with a given past actions record are sorted in increasing order, those corresponding to past actions records sharing the last action (C_last) and the fraction of cooperative actions () are statistically indistinguishable. This holds both for memory m = 3 (A) and memory m = 5 (B). (Labels nC|X denote memory records with last action X and n cooperative previous actions.) This implies that the reputation that players are taking into account is a weighted combination of C_last and , i.e., . The value of w can be obtained through a linear fit to the fractions of accepted link proposals as a function of r (C and D; see Methods and Supplementary Information for details). The results are w = 0.280 ± 0.024 for m = 3 and w = 0.165 ± 0.015 for m = 5. Notice that the weight for m = 5 can be obtained from the observation (B) that the fraction of accepted proposals for past action records 3C|D is statistically indistinguishable from that for past action records 1C|C. This implies (1 − w)(3/5) = (1 − w)(2/5) + w, i.e., w = 1/6 (compare with the value obtained through the linear fit).

Figure 3. Subjects try to hold a high reputation but not the highest.

The histogram of link lifetimes shows a fast exponential decay (A; average lifetimes are 2.75 rounds for m = 1, 3.21 for m = 3, and 3.23 for m = 5). This is a consequence of the fact that most individuals keep a record of 2 cooperative actions out of 3 (B) or 2–4 out of 5 (C); in other words, subjects often defect but not too much—that would ruin their reputation. But this sporadic defection has a drastic effect on the linking dynamics because reputation is very much influenced by subjects' last action.