Evidence of direct and indirect reciprocity in network-structured economic games

Abstract

Formal theoretical models propose that cooperative networks can be maintained when individuals condition behavior on social standing. Here, we empirically examine the predictions of such models of positive and negative indirect reciprocity using a suite of network-structured economic games in four rural Colombian communities (N_ind = 496 individuals, N_obs = 53,876 ratings/transfers). We observe that, at a dyadic-level, individuals have a strong tendency to exploit and punish others in bad standing (e.g., those perceived as selfish), and allocate resources to those in good standing (e.g., those perceived as generous). These dyadic findings scale to a more generalized, community level, where reputations for being generous are associated with receipt of allocations, and reputations for being selfish are associated with receipt of punishment. These empirical results illustrate the roles that both positive and negative reciprocity, and costly punishment, play in sustaining community-wide cooperation networks.

Fig. 1. Digraphs of two dyadic peer-ratings networks.

(a) shows generosity ratings, and (b) selfishness ratings---and behaviors of three network-structured economic games---(c) shows the outcome network of the Rich giving game, (d) the outcome of the RICH exploitation game, and (e) the outcome of the RICH punishment game---from the lowland community in rural Colombia (see Figs. S1–4 for corresponding plots from the other communities). Each network layer is dense, impeding visual assessments of network structure. To gain a better understanding of how perceptions of generosity and selfishness structure behavior in the game networks, we use hive plots in Fig. 2.

Fig. 2. Directed ties observed in each community during the three network-structured games.

Here, each hive plot^, represents a set of individuals ranked from bottom to top along each diagonal line in terms of their reputation measure: the sum total of nominations as generous minus the sum total of nominations as selfish. The ranking is smooth, but for visualization purposes we bin individuals into three separate reputation categories. This was done by coding individuals as having a `high' reputations when the count of their nominations for generosity exceeded their nominations for selfishness sufficiently, and vice versa for `low' reputation. Individuals viewed as more generous tend to give more, as is indicated by more lines flowing from higher up on the left-most axis. There is substantial variation in who receives allocations in each community---e.g., many poorer people, who could not afford to be as generous in the game, were still targets of giving. Exploitation is common in each community, and there is a clear signal that those with generous reputations preferentially exploit those with selfish reputations. Individuals of all reputational levels appear to punish at roughly equal rates, but people with selfish reputations are preferential targets of punishment.

Fig. 3. Dyad-level correlations in random effects.

Frame (a) plots posterior mean values of all dyadic correlation parameters from the lowland community organized in matrix form (See Figs S5, S7, S9 and S11 in the supplementary Materials for the plots for all communities). For example, we see that if individual j gave to individual k in the giving game, then individual j is reliably less likely to exploit individual k in the exploitation game (ρ = − 0.61). The left-most (gray) triangle of estimates gives within-person, between-layer correlations in dyadic random effects. The right-most (gray) triangle of estimates gives between-person, between-layer correlations in dyadic random effects. The diagonal set of estimates (black) gives within-layer dyadic reciprocity. Only reliable correlations are shown.Frame (b) shows the within-person, between-layer correlations as posterior means and 89% credible intervals (CI). Frame (c) Between-person, between-layer correlations as posterior means and 89% credible intervals. We note that social standing as generous is reliably associated with increased probability of receiving coins in the giving game, decreased probability of being exploited in the taking game, and decreased probability of being reduced in the costly punishment game. Likewise, social standing as selfish is reliably associated with decreased probability of receiving coins in the giving game, increased probability of being exploited in the taking game, and increased probability of being reduced in the costly punishment game.

Fig. 4. Generalized correlations in individual-level sender and receiver random effects (See Figs. S6, S8, S10 and S12 in the Supplementary Materials for the plots for all communities).

Frame (a) plots posterior mean values of all generalized reciprocity correlation parameters from the lowland community organized in matrix form. For example, we see that if an individual was on average a target of giving in the allocation game---see row labeled Give (Receiver)---then that same individual is also likely to be a target of high generosity ratings---see row labeled Generous (Receiver)---on average (ρ_l = 0.66). The upper-most (black) triangle of estimates gives generalized correlations in sender effects---e.g., if an individual tends to give to others overall, how likely are they to exploit others overall? The lower-most (black) triangle of estimates gives generalized correlations in receiver effects---e.g., if an individual tends to be given to by others overall, how likely are they to be exploited by others overall? The correlations between sender and receiver effects appear in the gray square region, but were not reliably non-zero in these models. Frames (b) and (c) provide posterior credible intervals for the effects outlined in frame (a). We note that generalized social standing as generous is reliably associated with increased probability of receiving coins in the giving game and decreased probability of being exploited in the taking game. Similarly, generalized social standing as selfish is reliably associated with an increased probability of being reduced in the costly punishment game.