Gossip: Perspective Taking to Establish Cooperation

Abstract

Problems of cooperation are frequent among living organisms, but they are difficult to solve. Humans have been able to produce large-scale cooperation among unrelated individuals through reputation systems. A challenging puzzle, however, is how reputation can guide behavior if in most cases it is not shared publicly and is assigned to others privately. We confirm that it is difficult to obtain cooperation among agents playing the Prisoner’s Dilemma when reputations are individually assigned. We propose that third-party communication (gossip) can overcome this difficulty, but only under specific conditions concerning its content, amount and persistence. We show that—in order to sustain cooperation—gossip should not only be about private evaluations of others but should also include perspective taking and exchange of information about tolerance thresholds to support cooperation. This perspective taking reputational strategy can propagate and establish cooperation in the population independent of gossip frequency and population size, under various selection mechanisms of communication partners and targets, and assumptions concerning agents’ memory.

Appendix A Materials and Methods

The agent-based model presented in this paper has been built in Matlab 2020b and is fully available on Github: (https://github.com/simonerighi/Gossip). The pseudocode of the model is reported in Section S4 of SI. Results reported summarize results of 100 runs for each parameter combination. Including all robustness checks, about 315000 individual simulations have been run.

Initialization: Population size N is fixed to 200 in the simulations reported in the figures and varied in the simulations reported in SI (Section S3), between 50 and 600. Initial strategies $c_{i}$, as well as the initial values for reputations $R_{iz}$ are generated at random from an uniform distribution between 0 and 100.

Choice of gossip partner: In the baseline model presented, an individual i chose to initiate gossip with an individual j chosen uniformly at random from the whole population. Other specifications of this process of partner selection are possible. In the supplementary material, we analyze the following ones: (1) j is chosen with probability (linearly) proportional to subjective reputation $R_{ij}$. (2-3) j is chosen from previous interaction partners uniformly at random or with probability proportional to $R_{ij}$. Options 1 and 3 imply that individuals have a preference to gossip with people to which they attribute high reputations. Options 2 and 3 simulate gossip based on recent interaction experience. All simulations presented in the main text are repeated in these setups and reported in SI, with nearly identical results.

Choice of gossip target: In the baseline model presented, the target individual z for gossip is selected uniformly at random from the whole population. Also in this case, several other specifications of this process are possible. We consider the following ones: (1) z is selected at random from people that interacted with i in the last interactions, (2) z is someone that i interacted with and did something surprising, with the surprise being defined as a mis-alignment between expectations about agent z based on reputation $R_{iz}$ and observed actions of z. In this case, the gossip target is chosen with probability proportional to $R_{iz}$ if z defected, and to 100-$R_{iz}$ if z cooperated. (3) z can be selected among individuals with similar reputation in the population, modeling status competition. Specifically, the probability of choosing the gossip target z is linearly proportional to $100- \vert \overline{R_{:,i}}-\overline{R_{:,z}} \vert$ (4) z is selected with inverse—linear—proportionality to its social reputation $\overline{R_{:,z}}$. All simulations presented in the main text are repeated in these setups and reported in SI, with nearly identical results.

Strategy (threshold) update: Once all interactions and gossip has taken place, each individual i observes its interacting partners’ payoffs and revises his threshold for cooperation $c_{i}$ toward the one of a, randomly selected, agent among those with a strictly payoff higher than its own. The revision can imply a maximum change of 10 points. Such choice has been made in order to ensure a smoother dynamics.