So there are several take-home lessons from the modules that we've looked at. We started off with Schelling and looked at the basic dynamics of segregation. One of the interesting implications there was individual choices that didn't have any preference for segregation, nevertheless, could lead to segregation. So there are sometimes unintended consequences of individual actions, and it's very hard for any individual to anticipate ahead of time what those consequences may be. Furthermore, for policymakers, it's hard to reason from individual choices to collective outcomes without some way of studying the aggregation dynamics that produce them. So building on this, we looked at the small world model, and what that showed was that when we look at the aggregation dynamics going from individual behaviors to collective outcomes, the interaction structure makes a difference in terms of how spreading works. So we saw there that long distance ties or weak ties in a network could dramatically accelerate the rate of diffusion. What's interesting there is that for any given individual network, it will be undetectable that the structure of the network could change. Nevertheless, these imperceptible differences and they connect in the population translate into very large, very significant effects for the dynamics of diffusion. Then, looking even deeper into the dynamics of behavior change and social network structure with the Complex Contagions. And there, what we saw is that although we had some very clear intuitions in a small worlds model and the weak ties theory about how long distance ties could accelerate diffusion, there's a really big difference between talking about information and disease diffusion versus behavior diffusion. We looked at behavior spreading. In fact, what we saw was that the networks that could accelerate disease actually slowed down the diffusion of behavior. And so there's a subtle interplay or interaction between a type of contagion that spreads and the complex dynamics of aggregation that lead to population change. Building on this, we look to the Emperor's dilemma. So this was a situation where people relied on social reinforcement to change behavior, but the behavior they were changing to was something they explicitly didn't want. And what we saw was that these local dynamics of reinforcement could transform a normal citizens in a society into false enforcers who could create a cascade of social enforcement that would carry an unpopular norm throughout a population. What we saw there was that a big lie is easier to spread than a small lie. The reason for this is that a big lie requires some demonstration of sincerity. A small lie can be complied with without any additional demonstrations, but a big lie is harder to believe. And so in order for people to really demonstrate their compliance with the norm, they have to go an extra step and enforce the norm, and this is what generates these large scale cascades. It also highlights the danger of these kinds of dynamics for getting really unpredictable and unlikely behaviors to spread to entire populations. So when we think about coordination at a population scale, we can also think about it in terms of the name game. So that's a situation where people work interacting locally and trying to coordinate with each other, normally, any arbitrary convention, but the space of options was unbounded. Unlike the Emperor's dilemma where a convention was seeded by a few rogues, this is a situation where people could choose any option they wanted. All they wanted to do was to figure out a coordination norm with their neighbors. Through this process of local interactions, the network structure of how they interacted mediated how quickly and how effectively the population would reach convergence. And in the final module, we looked at problem solving, and took the idea of rapid coordination and highly efficient, highly connected networks, and thought about what it meant for the quality of the coordination on the people achieved. In particular, when people are trying to solve difficult problems and they coordinate very effectively, does that lead to better solutions or worse solutions? And what we saw is that whereas exploitation can be very effective for moving populations to coordinate very quickly on a solution, this is only beneficial if the population is working on a simple problem where there's one obvious solution. If the problem space is more complex and it's a difficult to explore, then actually having less efficient communication networks can encourage exploration and allow populations over time to move towards a much better solution than could have been discovered otherwise. Overall, when we think about all these different kinds of problems and how they tied together from the unintended consequences of individuals interacting locally to the dynamics of norms spreading to the network structures that accelerate or slow down the spread of norms to the kinds of solutions, the quality of the decisions that populations ultimately make, we can also think about what all of these kinds of models mean for studying collective behavior empirically. So one of the things we'll talk about in a different course is how to think about these things experimentally, how to study the collective dynamics of behavior change in large populations using humans instead of agent actors.