In this lecture, we review topics that might be covered on the Spring 2023 final exam of SOS 220 (Systems Thinking). This involves going back to reviewing concepts from resilience thinking about dynamical systems to topics in network science to topics in game-theoretic modeling of social systems. We also review the relationship between the second law of thermodynamics and closed thermodynamic systems as well as some basic terms in the biology of inheritance and natural selection.
In this lecture, we wrap up the course by connecting the networking thinking from the previous unit to the resilience thinking introduced earlier in the course. We first cover scale-free networks as a particular kind of small-world network with a notable (and apparently very natural) degree distribution. This helps motivate that metrics of networks can be informative about the processes that are driving the structure of those networks. This lets us pivot to a relatively new result testing the stress-gradient hypothesis in mixed-species bird flocks in South America. That study shows that with increased stresses, social networks of species within observed bird flocks become more connected (and less modular). We connect this observation to previous units on the adaptive cycle and panarchy as well as the current chapter on using resilience thinking for sustainability problems. In particular, we discuss how diversity is an asset in communities under stresses that reduce competitive structure (i.e., diversity increases the robustness of the communities to stressors); however, when there is low stress, communities tend to be shaped by competitive exclusion (and efficiency maximization).
Comments in this lecture were motivated by Walker and Salt (2006, Chapter 6), which presents 9 hypothetical attributes of resilient (and sustainable) societies which are built around "creating space" in those societies/organizations.
In this lecture, we finish up our discussion of the Hawk–Dove (chicken) model as a game-theoretic exploration of commons/common-pool resources problems (and the tragedy of the commons). We contrast the Hawk–Dove with the stag hunt (public goods problem). Putting them together helps illustrate the idea of "network effects" from economics and motivates why looking at "networks" more formally might lead to understanding other macroscale phenomena. That lets us transition to Stanley Milgram and his experiment with letters that led to the "six degrees of separation" "small-world network" observation about human society. We discuss how network science provides a formal set of tools behind this network thinking and then provide the graph-theoretic ideas necessary to speak this language (nodes, edges, hubs, clusters, degree, degree distribution, etc.). We use Google PageRank as an example of how degree can be a useful tool for differentiating between nodes in a network and then start to discuss a formal definition of small-world networks and, eventually, scale-free networks. We will finish discussing scale-free networks in the next lecture.
This lecture is based on topics from Chapters 15 and 16 from Melanie Mitchell's 2009 Complexity book.
In this lecture, we review the classic "Prisoner's Dilemma" game-theoretic model of the challenges of cooperation in a world of strong temptation to defect, and then we contrast it with two other models that are possibly more realistic (but similarly simple) models of cooperation and competition in the real world -- the stag hunt model and the Hawk–Dove model. The stag hunt is a model of positive externalities, like those that characterize public goods games. We discuss how the stag hunt is like a Prisoner's Dilemma with a stronger reward for cooperation (stronger positive externalities) than a temptation to defect. This lets us introduce coordination games, assurance games, and correlated equilibria. In general, the stag hunt shows us that there are more fundamental issues to cooperation beyond incentives -- there are barriers to the coordination of actions and information limitations that prevent cooperation even when it is favored. We extend the stag hunt to the N-player stag hunt, which is a better model of public goods problems, in order to introduce the idea of a mixed (Nash) equilibrium. We then close with an introduction of the Hawk–Dove game, which is a model of competition and negative externalities that often characterize common-pool resources problems ("tragedies of the commons"). We will continue discussion of the Hawk–Dove next time and explore why it is a better match to tragedy of the commons problems than the Prisoner's Dilemma.
In this lecture, we review the key results from the computational tournaments run by Robert Axelrod on the iterated/repeated Prisoner's dilemma game. We re-introduce the Prisoner's dilemma and the puzzle of how cooperation can evolve, identifying the difference between the Nash equilibrium and a socially efficient solution that is not a Nash equilibrium as being the key problem. This lets us talk about resolutions to the problem – including relatedness and compensation. We then discuss how iterating the Prisoner's Dilemma introduces temporal relatedness, and how placing the Prisoner's Dilemma on a grid introduces network relatedness. After mentioning how punishment can also be used to maintain cooperation in Prisoner's Dilemma games, we open the topic of how the Prisoner's Dilemma may be unrealistic and other games might be better/more useful models, particularly when it comes to natural resources and sustainability. We close with a brief introduction to the Stag Hunt coordination game, which we will pick up on next time (as well as introduce the Hawk–Dove game, which is a better model for the tragedy of the commons than the Prisoner's Dilemma).
In this lecture, we discuss topics related to "Prospects of Computer Modeling" by Mitchell (2009, Chapter 14). We start with a discussion of what it means for complex systems science to be a science. We follow that with a re-introduction to the scientific process, where we make things like causal questions, hypotheses, experiments, models, predictions, and theories explicit. We focus a lot on how hypotheses are answers to causal how/why questions and are NOT if–then statements (which are predictions). After going through the scientific process, we introduce the computational social simulation of the evolution of cooperation (starting with Robert Axelrod's popular efforts) and the prisoner's dilemma model. We do not quite get to the main computational results from Axelrod's study, which we will touch on at the start of the next lecture. We do discuss the requirements for a game to be a prisoner's dilemma and how the Nash equilibrium of the prisoner's dilemma is not Pareto efficient, which makes it a good model for such traps as the tragedy of the commons.
In this lecture, we continue to discuss the different ways to search for and process information from the environment in distributed architectures in nature. Whereas the last lecture focused on nonlinear recruitment strategies (and more generally strategies focused on trail laying and external memory), this lecture focusses on linear recruitment strategies such as the honeybee waggle dance (and piping transition in the case of nest-site selection) and the ant tandem run (and transition to transport in the case of nest-site selection). After demonstrating the waggle dance, the tandem run, and the differences between individual and group performance in decision-making tasks, the lecture closes discussing different mechanistic models for how individual ants decide when to transition from tandem run to transport.
DUE TO TECHNICAL ISSUES IN THE ROOM, there are small parts of this lecture where the audio or video will drop out.
