What makes team work?
Source: Triadic Balance and Closure as Drivers of the Evolution of Cooperation
Simone Righi and Karoly Takacs of the Hungarian Academy of Sciences published this study in 2014. Their question, at the broadest level, is why do people work together? So many people believe that the only way to get ahead in this eye-for-an-eye world is to only look out for only yourself. Yet most people work together and there is so much kindness shown every day. Society has been built on a foundation of cooperation.
Social networks are constantly changing and we have only barely scratched the surface of the mechanisms that drive their dynamics. Triadic closure and triadic balance is the mechanism that they are looking at in this study. When bonds form between two agents, it can be positive or negative. So, through models and extensive simulations, Righi and Takacs generate a social structure where there are two options for each agent, cooperate or defect. In this study, they are treated as completely unconditional options, which does not translate exactly into the real world, but is a good basis for starting to look at this problem.
When testing triadic closure, the simulation would find three agents i, j, and k, where i cooperates with j and k, but there is no relationship between j and k. Then create a random link between j and k, either cooperate or defect, and remove a random link of the same relationship from another part of the graph to retain the same density of relationships.
Then, they go in and make sure that the data satisfies triadic balance. Each link is checked, and if it is unstable, it is changed to the relationship that will balance the triad.
In order to measure the benefits of each option for the agents, a payoff matrix from a previously established study was used to calculate each agent’s payoff by the end of the simulation.
Using that, they carry out an “evolutionary mechanism” that allows each agent to look around, see which strategy has worked out the best, and then either change or stay based on the payoffs.
When the triadic closures and triadic balances are not enforced, almost all of the cooperative ties are gone after the evolutionary mechanism. However, there is a statistically significant increase in the amount of cooperative ties left after carrying out the evolutionary mechanism on triadically closed and balanced nodes. According to these simulations, if a society does not exhibit triadic closure or balance, there would be no increase in payoff for cooperation and all nodes would eventually stabilize around defection.
This winds up reflecting exactly what we have heard in lecture: networks are more stable when they fit the two models of triadic balance. When this balance is reached, nodes tend to not want to leave the state that they are in. And the triadic closure property is one that we have discussed extensively during class.