Article Figures & Data
Figures
- Figure 1.
The results for the effects of oxytocin on trust in a repeated trust game network. a, Participant assignment before the experiment. For each network, three participants were randomly assigned as the central nodes and were invited into behavioral testing room A for oxytocin/placebo administration 35 min before the network experiments. Then, all the central and other peripheral players were invited into network testing room B at the same time and randomly assigned to individual cubicles for the experiment. b, Network structure and rules. Each TG network consisted of 18 participants, with 9 trustees (blue-filled circle) and 9 investors (yellow-filled circles indicate central investors, and gray-filled circles indicate peripheral investors). In each TG round, an investor made a single investment t (0 ≤ t ≤ 100) in all of his or her neighboring trustees. Trustees received the tripled amount, 3t, and had to decide on one single return rate r (0 ≤ r ≤ 1) that would apply to all of his or her neighboring investors. c–e, The administration of oxytocin enhanced the investment of central investors (c), but influenced neither the return rate of trustees (d) nor the investment of peripheral investors (e). The test statistics shown in the figure are based on two-tailed independent-sample t tests comparing oxytocin and placebo networks with *p < 0.05, n.s., not significant. Data are plotted as box plots for each condition, with horizontal lines indicating median values, fixation indicating mean values, boxes indicating 25% and 75% quartiles, and whiskers indicating the 2.5–97.5% percentile range. The round-by-round dynamics of decisions over time are presented on the right side of each box plot with each solid line representing the mean value of each round and shading showing the 95% CI.
- Figure 2.
Effects of oxytocin on the ultimate bargaining network. a, Network structure and interaction rules. Each network consisted of 18 participants, with 9 proposers (blue-filled circle) and 9 responders (central responders, yellow-filled circles; peripheral responders, gray-filled circles). In each UBG round, a proposer made one single offer, poffer, to all of his/her neighboring responders, and a responder decided on one single minimum acceptance level, raccept, that would apply to all of their neighboring proposers. For each connection, the deal with one neighbor was made only if poffer ≥ raccept; otherwise, both received 0. b, Global fairness (poffer) dynamics across the 60 rounds of the UBG. In oxytocin (vs placebo) networks, global fairness was significantly higher. c, Oxytocin significantly increased payoff equality between proposers and responders. d, Conceptual illustration and real strategy choices of proposers. Each proposer received responses from four neighboring responders with different levels of acceptance. Proposers would make all deals succeed when their offer matched the highest acceptance level (rmax) among neighboring responders. Proposers indeed matched the highest acceptance level of responders in 80.3% of the rounds (poffer ≥ rmax, purple dots). e, f, Oxytocin enhanced rmax (e), and between-network mediation analyses (f) showed that the effect of oxytocin on changes in poffer was mediated by rmax. g, h, Oxytocin induced a higher rmax in central responders (rmax central; g) but not in peripheral responders (rmax peripheral; h). i, However, with the increased enforcement of fairness by central players given oxytocin, peripheral players also increased maximum demand for a fair distribution of resources over time (indicated by the increased slope of rmax peripheral). Data are plotted as box plots for oxytocin and placebo networks, with horizontal lines indicating median values, fixation indicating mean values, boxes indicating 25% and 75% quartiles, and whiskers indicating the 2.5–97.5% percentile range. The round-by-round dynamics of decisions over time are presented on the left side of the box plot, with each solid line representing the mean value of each round and shading showing the 95% CI. *p < 0.05, **p < 0.01, n.s., not significant.
- Figure 3.
Effects of oxytocin on the two-stage prisoner's dilemma network. a, Network structure and interaction rules. Each tPDG network consisted of 12 participants: 3 central players (yellow-filled circle) played the tPDG game with 8 neighbors (2 central players and 6 peripheral players), and 9 peripheral players (gray-filled circles) played the tPDG game with 4 neighbors (2 central players and 2 peripheral players). In each tPDG round, participants made decisions to either cooperate (C) or defect (D) in stage I, received feedback on the number of neighbors choosing C/D and, then, in stage II, decided whether to punish (P) their defecting neighbors or not punish (NP). b, Cooperation rate of the network across the 30 tPDG rounds. b–d, The administration of oxytocin to the three central players increased the cooperation rate (b), decreased the number of defect–defect decision pairs (c), and elevated the punishment rate of the whole network (d). e, f, Peripheral players' cooperation rate (e) and punishment rate (f) were increased in the oxytocin (vs placebo) networks. g, h, Central players in the oxytocin (vs placebo) networks showed more nonpunishing cooperation (g), but also decreased their punishment behaviors less over time (h). i, j, Punishment from central players led to the increased cooperation (i) and punishment (j) of peripheral players in oxytocin (vs placebo) networks. Data are plotted as box plots for oxytocin and placebo networks, with horizontal lines indicating median values, fixation indicating mean values, boxes indicating 25% and 75% quartiles, and whiskers indicating the 2.5–97.5% percentile range. The round-by-round dynamics of decisions over time are presented on the left side of the box plot, with each solid line representing the mean value of each round and shading showing the 95% CI. *p < 0.05, † 0.05<p < 0.1.
- Figure 4.
Evolution of peripheral cooperation when central nodes vary in cooperation and punishment rate. a, b, Cooperation rate of the periphery of the network depending on the punishment rate and cooperation rate of central nodes in the simulated agent-based networks. The networks in each corner illustrate the cooperation rate of all peripheral agents in the network based on high/low central cooperation/punishment. The slope analysis of isoclines (of cooperation rate in a two-dimensional parameter space of cooperation and punishment) showed that central cooperators failed to affect the rest of the population when they seldomly punished (slope = 0 when p = 0.20). In contrast, central cooperation is as effective as punishment only if cooperation is enforced by moderate to strong punishment (slope = 1 when p = 0.39). c, d, The evolutionary dynamics of the strategies used by the peripheral nodes with high (c) or low (d) central punishment. Whereas the always-cooperate strategy was favored in the ClowPhigh condition, punitive cooperators (ChighPhigh) in the central position facilitated the use of conditional cooperation (i.e., tit-for-tat strategy) and punishment strategies (i.e., always-punish and conditionally punish strategies) in the peripheral nodes. With low central punishment, only always-defect combined with always-nonpunish strategy slightly outperformed other strategies in peripheral players, regardless of the cooperation level of central nodes (ClowPlow and ChighPlow). e, An alternative evolutionary model that manipulates peripheral nodes shows a much weaker effect on global cooperation. f, g, Cooperation rate of the periphery of the network depending on central punishment and cooperation rates in networks with population sizes of 40 (f) and 100 (g). Cooperation outcomes of alternative population sizes reveal the same pattern. highC, high cooperation rate; lowC, low cooperation rate; highP, high punishment rate; lowP, low punishment rate; always C, always-cooperate; always D, always-defect; always P, always-punish; conditionally P, conditionally-punish; always NP, always-non-punish.
- Figure 5.
Consistent results of the alternative agent-based models with varied heterogeneity degree, selection strength, cost ratio, and the number of central-to-central connections. a–c, Cooperation rate of the periphery of the network depending on the punishment rate (x-axis) and cooperation rate (y-axis) of central nodes in the simulated agent-based networks where the heterogeneity degree equals 5:3 (i.e., central nodes are connected with five nodes and peripheral nodes are connected with three nodes; a), selection strength equals 6 or 10 (b), or cost ratio equals 2:4 or 2:5 (c), while other parameters remain unchanged. Changes in these parameters revealed the same pattern that altering the punishment propensity of central nodes is more powerful than altering cooperation rates in increasing peripheral cooperation. d–f, Results of the alternative agent-based models with 2 (d), 1 (e), and 0 (f) central-to-central connections, with descending synchronization effect of the central community (central community even disappeared in models in e and f). The patterns of cooperation spread was qualitatively insensitive to the rich-club coefficient and remained similar as the original model in these alternative models (black lines, central–central connections; pink lines, central–peripheral connections; blue lines, peripheral–peripheral connections). highC, high cooperation rate; lowC, low cooperation rate; highP, high punishment rate; lowP, low punishment rate.
- Figure 6.
Results of the alternative agent-based models with varied numbers of manipulated central nodes and central coverage. a, b, With the same network structure as the original model, we manipulated cooperation/punishment rates only for two central nodes (a) or one central node (b). c, d, With the same number of 12 nodes and 30 edges as the original model, we changed the number of central nodes: 2 central nodes (c) or 1 central node (d) in alternative models. We found central nodes to be less influential on altering global cooperation when decreasing the number of central nodes. Specifically, the pattern remained similar when manipulating cooperation/punishment rated for two central nodes (a, c). However, when the cooperation/punishment rates were manipulated on only one central node, the cooperation spreading effect disappeared (b, d). e, f, Results of alternative agent-based models when manipulating peripheral nodes with the same coverage. e, Network structures with the same 15 (of 30) directly influenced connections (red lines). To achieve 50% coverage of manipulated nodes, we manipulated the cooperation/punishment rate of two central nodes (i.e., nodes 1 and 2) or four peripheral nodes (i.e., nodes 6, 8, 9, 11; red circles). The number of central, peripheral nodes, and the number of directly influenced connections, and the structures were the same as in these two models. Yellow circles, Unmanipulated central nodes; blue circles, unmanipulated peripheral nodes; blue lines, connections between unmanipulated nodes. f, Although we manipulated more peripheral nodes, manipulations of peripheral nodes resulted in a similar but much weaker tendency of the cooperation/punishment influence. Black lines, Central–central connections; pink lines, central–peripheral connections; blue lines, peripheral–peripheral connections. highC, high cooperation rate; lowC, low cooperation rate; highP, high punishment rate; lowP, low punishment rate.
Extended Data
Figure 1-1
Experimental instructions for experiments 1–3. Download Figure 1-1, DOCX file.
