Fig. 2: Dynamic networks produce (anti-)correlated interactions that lead to spite.

a ‘Spiteful’ fixates at the final time-step of our model over a range of population sizes, and b imitation rates. c The local network learning process of each agent changes the likelihood of each of the possible pairwise interactions over time (plotted by seed). ‘Spiteful’ agents learn to target ‘Social’ agents, who provide the highest payoff, and not each other. Similarly, but inversely, ‘Social’ agents learn to target each other, and to avoid ‘Spiteful’ agents. d The network learning process significantly improves the median average payoff of ‘Spiteful’ agents (d–f averages over 200 simulations). e The system level result of these local learning processes is the formation of positively correlated interaction patterns among ‘Social’ agents, anti-correlated interaction patterns among ‘Spiteful’ agents, and relatively neutral overall correlated interactions. f Under the interaction patterns emerging in the model, if the ratio b to c is sufficiently large, then spite emerges. Interestingly, the standard condition for the invasion and stability of spite, overall correlated interactions below −c/b, does not need to be satisfied for the ‘Spiteful’ strategy to emerge in our model.